A387181 -id:A387181 - cp's OEIS frontend

A387120 Number of ways to choose a different constant integer partition of each prime index of n.

1, 1, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 4, 3, 4, 0, 2, 2, 4, 0, 6, 2, 3, 0, 2, 4, 0, 0, 4, 4, 2, 0, 4, 2, 6, 0, 6, 4, 8, 0, 2, 6, 4, 0, 4, 3, 4, 0, 6, 2, 4, 0, 5, 0, 4, 0, 8, 4, 2, 0, 6, 2, 6, 0, 8, 4, 2, 0, 6, 6, 6, 0, 4, 6, 4, 0, 6, 8, 4, 0, 0, 2, 2, 0, 4, 4, 8

Offset: 1

Gus Wiseman, Aug 26 2025

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

			The prime indices of 90 are {1,2,2,3}, with choices:
  ((1),(2),(1,1),(3))
  ((1),(1,1),(2),(3))
  ((1),(2),(1,1),(1,1,1))
  ((1),(1,1),(2),(1,1,1))
so a(90) = 4.

For multiset systems see A355529, set systems A367901.
For not necessarily different choices we have A355731, see A355740.
For divisors instead of constant partitions we have A355739 (also the disjoint case).
For prime factors instead of constant partitions we have A387136.
For all instead of just constant partitions we have A387110, disjoint case A383706.
For initial intervals instead of partitions we have A387111.
For strict instead of constant partitions we have A387115.
Twice partitions of this type are counted by A387179, constant-block case of A296122.
Positions of zero are A387180 (non-choosable), complement A387181 (choosable).
A000041 counts integer partitions, strict A000009.
A003963 multiplies together prime indices.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
Cf. A000005, A063834, A261049, A299200, A299201, A335433, A335448, A355741, A357977, A387135.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Length[Select[Tuples[Select[IntegerPartitions[#],SameQ@@#&]&/@prix[n]],UnsameQ@@#&]],{n,100}]

A387137 Number of integer partitions of n whose parts do not have choosable sets of strict integer partitions.

Original entry on oeis.org

0, 0, 1, 1, 3, 4, 6, 9, 14, 20, 29, 39, 56, 74, 101, 134, 178, 232, 305, 392, 508, 646, 825, 1042, 1317, 1649, 2066, 2567, 3190, 3937, 4859, 5960, 7306, 8914, 10863, 13183, 15984, 19304, 23288, 28003, 33631, 40272, 48166, 57453, 68448, 81352, 96568, 114383

Offset: 0

Gus Wiseman, Sep 02 2025

We say that a sequence of nonempty sets is choosable iff it is possible to choose a different element from each set. For example, ({1,2},{1},{1,3}) is choosable because we have the choice (2,1,3), but ({1},{2},{1,3},{2,3}) is not.
a(n) is the number of integer partitions of n such that it is not possible to choose a sequence of distinct strict integer partitions, one of each part.
Also the number of integer partitions of n with at least one part k whose multiplicity exceeds A000009(k).

			The a(2) = 1 through a(8) = 14 partitions:
  (11)  (111)  (22)    (221)    (222)     (322)      (422)
               (211)   (311)    (411)     (511)      (611)
               (1111)  (2111)   (2211)    (2221)     (2222)
                       (11111)  (3111)    (3211)     (3221)
                                (21111)   (4111)     (3311)
                                (111111)  (22111)    (4211)
                                          (31111)    (5111)
                                          (211111)   (22211)
                                          (1111111)  (32111)
                                                     (41111)
                                                     (221111)
                                                     (311111)
                                                     (2111111)
                                                     (11111111)

The complement for initial intervals is A238873, ranks A387112.
The complement for divisors is A239312, ranks A368110.
Twice-partitions of this type (into distinct strict partitions) are counted by A358914.
For divisors instead of strict partitions we have A370320, ranks A355740.
The complement for prime factors is A370592, ranks A368100.
For prime factors instead of strict partitions we have A370593, ranks A355529.
For initial intervals instead of strict partitions we have A387118, ranks A387113.
For all partitions instead of strict partitions we have A387134, ranks A387577.
These partitions are ranked by A387176.
The complement is counted by A387178, ranks A387177.
The complement for partitions is A387328, ranks A387576.
The version for constant partitions is A387329, ranks A387180.
The complement for constant partitions is A387330, ranks A387181.
A000005 counts divisors.
A000041 counts integer partitions, strict A000009.
A367902 counts choosable set-systems, complement A367903.
Cf. A005703, A052335, A261049, A270995, A276078, A335448, A355535, A367867, A367901, A367905, A383706, A387115.

strptns[n_]:=Select[IntegerPartitions[n],UnsameQ@@#&];
Table[Length[Select[IntegerPartitions[n],Length[Select[Tuples[strptns/@#],UnsameQ@@#&]]==0&]],{n,0,15}]

A387176 Numbers whose prime indices do not have choosable sets of strict integer partitions. Zeros of A387115.

Original entry on oeis.org

4, 8, 9, 12, 16, 18, 20, 24, 27, 28, 32, 36, 40, 44, 45, 48, 52, 54, 56, 60, 63, 64, 68, 72, 76, 80, 81, 84, 88, 90, 92, 96, 99, 100, 104, 108, 112, 116, 117, 120, 124, 125, 126, 128, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 162, 164, 168, 171, 172

Offset: 1

Gus Wiseman, Aug 27 2025

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We say that a sequence of nonempty sets is choosable iff it is possible to choose a different element from each set. For example, ({1,2},{1},{1,3}) is choosable because we have the choice (2,1,3), but ({1},{2},{1,3},{2,3}) is not.

The complement for all partitions appears to be A276078, counted by A052335.
For all partitions we appear to have A276079, counted by A387134.
For divisors instead of strict partitions we have A355740, counted by A370320.
Twice-partitions of this type (into distinct strict partitions) are counted by A358914.
The complement for divisors is A368110, counted by A239312.
The complement for initial intervals is A387112, counted by A238873, see A387111.
For initial intervals instead of strict partitions we have A387113, counted by A387118.
These are the positions of 0 in A387115.
Partitions of this type are counted by A387137, complement A387178.
The complement is A387177.
The version for constant partitions is A387180, counted by A387329.
The complement for constant partitions is A387181, counted by A387330.
A000041 counts integer partitions, strict A000009.
A003963 multiplies together the prime indices of n.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
Cf. A000720, A261049, A270995, A335433, A335448, A355744, A357978, A357980, A383706, A387110, A387120.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Select[Tuples[Select[IntegerPartitions[#],UnsameQ@@#&]&/@prix[#]],UnsameQ@@#&]=={}&]

A387177 Numbers whose prime indices have choosable sets of strict integer partitions. Positions of nonzero terms in A387115.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98

Offset: 1

Gus Wiseman, Aug 29 2025

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We say that a sequence of nonempty sets is choosable iff it is possible to choose a different element from each set. For example, ({1,2},{1},{1,3}) is choosable because we have the choice (2,1,3), but ({1},{2},{1,3},{2,3}) is not.

			The prime indices of 50 are {1,3,3}, and {(1),(3),(2,1)} is a valid choice of distinct strict partitions, so 50 is in the sequence.

The version for all partitions appears to be A276078, counted by A052335.
The complement for all partitions appears to be A276079, counted by A387134.
The complement for divisors is A355740, counted by A370320.
Twice-partitions of this type (into distinct strict partitions) are counted by A358914.
The version for divisors is A368110, counted by A239312.
The version for initial intervals is A387112, counted by A238873, see A387111.
The complement for initial intervals is A387113, counted by A387118.
These are the positions of nonzero terms in A387115.
The complement is A387176.
Partitions of this type are counted by A387178, complement A387137.
The complement for constant partitions is A387180, counted by A387329, see A387120.
The version for constant partitions is A387181, counted by A387330.
A000041 counts integer partitions, strict A000009.
A003963 multiplies together the prime indices of n.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A289509 lists numbers with relatively prime prime indices.
Cf. A000720, A120383, A270995, A299200, A335433, A335448, A357978, A357982, A383706, A387110.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
strptns[n_]:=Select[IntegerPartitions[n],UnsameQ@@#&];
Select[Range[100],Select[Tuples[strptns/@prix[#]],UnsameQ@@#&]!={}&]

A387178 Number of integer partitions of n whose parts have choosable sets of strict integer partitions.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 5, 6, 8, 10, 13, 17, 21, 27, 34, 42, 53, 65, 80, 98, 119, 146, 177, 213, 258, 309, 370, 443, 528, 628, 745, 882, 1043, 1229, 1447, 1700, 1993, 2333, 2727, 3182, 3707, 4311, 5008, 5808, 6727, 7782, 8990, 10371, 11952, 13756, 15815, 18161

Offset: 0

Gus Wiseman, Sep 02 2025

First differs from A052337 in having 745 instead of 746.
We say that a sequence of nonempty sets is choosable iff it is possible to choose a different element from each set. For example, ({1,2},{1},{1,3}) is choosable because we have the choice (2,1,3), but ({1},{2},{1,3},{2,3}) is not.
a(n) is the number of integer partitions of n such that it is possible to choose a sequence of distinct strict integer partitions of each part.
Also the number of integer partitions of n with no part k whose multiplicity exceeds A000009(k).

			The partition y = (3,3,2) has sets of strict integer partitions ({(2,1),(3)},{(2,1),(3)},{(2)}), and we have the choice ((2,1),(3),(2)) or ((3),(2,1),(2)), so y is counted under a(8).
The a(1) = 1 through a(9) = 10 partitions:
  (1)  (2)  (3)    (4)    (5)    (6)      (7)      (8)      (9)
            (2,1)  (3,1)  (3,2)  (3,3)    (4,3)    (4,4)    (5,4)
                          (4,1)  (4,2)    (5,2)    (5,3)    (6,3)
                                 (5,1)    (6,1)    (6,2)    (7,2)
                                 (3,2,1)  (3,3,1)  (7,1)    (8,1)
                                          (4,2,1)  (3,3,2)  (4,3,2)
                                                   (4,3,1)  (4,4,1)
                                                   (5,2,1)  (5,3,1)
                                                            (6,2,1)
                                                            (3,3,2,1)

For initial intervals instead of strict partitions we have A238873, ranks A387112.
For divisors instead of strict partitions we have A239312, ranks A368110.
The complement for divisors is A370320, ranks A355740.
For prime factors instead of strict partitions we have A370592, ranks A368100.
The complement for prime factors is A370593, ranks A355529.
The complement for initial intervals is A387118, ranks A387113.
The complement for all partitions is A387134, ranks A387577.
The complement is counted by A387137, ranks A387176.
These partitions are ranked by A387177.
For all partitions instead of just strict partitions we have A387328, ranks A387576.
The complement for constant partitions is A387329, ranks A387180.
For constant partitions instead of strict partitions we have A387330, ranks A387181.
A000041 counts integer partitions, strict A000009.
A358914 counts twice-partitions into distinct strict partitions.
A367902 counts choosable set-systems, complement A367903.
Cf. A005703, A052335, A261049, A270995, A276078, A335448, A367867, A367901, A387115.

strptns[n_]:=Select[IntegerPartitions[n],UnsameQ@@#&];
Table[Length[Select[IntegerPartitions[n],Select[Tuples[strptns/@#],UnsameQ@@#&]!={}&]],{n,0,15}]

A387180 Numbers of which it is not possible to choose a different constant integer partition of each prime index.

Original entry on oeis.org

4, 8, 12, 16, 20, 24, 27, 28, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 125, 128, 132, 135, 136, 140, 144, 148, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 200, 204

Offset: 1

Gus Wiseman, Aug 30 2025

First differs from A276079 in having 125.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
Also numbers n with at least one prime index k such that the multiplicity of prime(k) in the prime factorization of n exceeds the number of divisors of k.

			The prime indices of 60 are {1,1,2,3}, and we have the following 4 choices of constant partitions:
  ((1),(1),(2),(3))
  ((1),(1),(2),(1,1,1))
  ((1),(1),(1,1),(3))
  ((1),(1),(1,1),(1,1,1))
Since none of these is strict, 60 is in the sequence.
The prime indices of 90 are {1,2,2,3}, and we have the following 4 strict choices:
  ((1),(2),(1,1),(3))
  ((1),(2),(1,1),(1,1,1))
  ((1),(1,1),(2),(3))
  ((1),(1,1),(2),(1,1,1))
So 90 is not in the sequence.

For prime factors instead of constant partitions we have A355529, counted by A370593.
For divisors instead of constant partitions we have A355740, counted by A370320.
The complement for prime factors is A368100, counted by A370592.
The complement for divisors is A368110, counted by A239312.
The complement for initial intervals is A387112, counted by A238873.
For initial intervals instead of partitions we have A387113, counted by A387118.
These are the positions of zero in A387120.
For strict instead of constant partitions we have A387176, counted by A387137.
The complement for strict partitions is A387177, counted by A387178.
Twice-partitions of this type are counted by A387179, constant-block case of A296122.
The complement is A387181 (nonzeros of A387120), counted by A387330.
Partitions of this type are counted by A387329.
A000041 counts integer partitions, strict A000009.
A003963 multiplies together prime indices.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
Cf. A355739, A367771, A387111, A387115.
Cf. A000005, A052335, A063834, A276079, A299200, A299201, A335433, A335448, A355731, A383706, A387110.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Select[Tuples[Select[IntegerPartitions[#],SameQ@@#&]&/@prix[#]],UnsameQ@@#&]=={}&]

A387329 Number of integer partitions of n such that it is not possible to choose a different constant integer partition of each part.

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 6, 8, 12, 18, 26, 35, 50, 67, 92, 122, 164, 214, 282, 364, 472

Offset: 0

Gus Wiseman, Sep 05 2025

			The a(2) = 1 through a(8) = 12 partitions:
  (11)  (111)  (211)   (311)    (222)     (511)      (611)
               (1111)  (2111)   (411)     (2221)     (2222)
                       (11111)  (2211)    (3211)     (3311)
                                (3111)    (4111)     (4211)
                                (21111)   (22111)    (5111)
                                (111111)  (31111)    (22211)
                                          (211111)   (32111)
                                          (1111111)  (41111)
                                                     (221111)
                                                     (311111)
                                                     (2111111)
                                                     (11111111)

For divisors instead of constant partitions we have A370320, complement A239312.
For all (not just constant) partitions we have A387134, ranks A387577.
The complement all partitions is A387328, ranks A387576.
The complement strict partitions is A387178.
For strict (not just constant) partitions we have A387137.
These partitions are ranked by A387180.
The complement is A387330, ranked by A387181.
A000005 counts constant integer partitions.
A000009 counts strict integer partitions.
A000041 counts integer partitions.
Cf. A052335, A063834, A335448, A355739, A387110, A387115.

consptns[n_]:=Select[IntegerPartitions[n],SameQ@@#&];
Table[Length[Select[IntegerPartitions[n],Select[Tuples[consptns/@#],UnsameQ@@#&]=={}&]],{n,0,15}]

A387330 Number of integer partitions of n such that it is possible to choose a different constant integer partition of each part.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 5, 7, 10, 12, 16, 21, 27, 34, 43, 54, 67, 83, 103, 126, 155, 188, 229, 277, 335, 403, 483, 578, 691, 821, 975, 1155, 1367, 1610, 1896, 2228, 2613, 3057, 3573, 4167, 4853, 5640, 6550, 7590, 8786, 10154, 11722, 13510, 15556, 17885, 20540

Offset: 0

Gus Wiseman, Sep 07 2025

Also the number of integer partitions of n such that for each part k the multiplicity of k is at most A000005(k).

			The partition (4,2,2,1) has choices such as ((2,2),(1,1),(2),(1)) so is counted under a(9).
The a(1) = 1 through a(9) = 12 partitions:
  (1)  (2)  (3)   (4)   (5)    (6)    (7)    (8)     (9)
            (21)  (22)  (32)   (33)   (43)   (44)    (54)
                  (31)  (41)   (42)   (52)   (53)    (63)
                        (221)  (51)   (61)   (62)    (72)
                               (321)  (322)  (71)    (81)
                                      (331)  (332)   (432)
                                      (421)  (422)   (441)
                                             (431)   (522)
                                             (521)   (531)
                                             (3221)  (621)
                                                     (3321)
                                                     (4221)

For initial intervals instead of constant partitions we have A238873, complement A387118.
For divisors instead of constant partitions we have A239312, complement A370320.
The complement for all partitions is A387134, ranks A387577.
The complement for strict partitions is A387137.
For strict instead of constant partitions we have A387178.
These partitions are ranked by A387181.
For all partitions (not just constant) we have A387328, ranks A387576.
The complement is counted by A387329, ranks A387180.
A000005 counts constant integer partitions.
A000009 counts strict integer partitions.
A000041 counts integer partitions.
A063834 counts twice-partitions.
Cf. A052335, A276079, A355731, A355739, A367771, A383706, A387110.

consptns[n_]:=Select[IntegerPartitions[n],SameQ@@#&];
Table[Length[Select[IntegerPartitions[n],Select[Tuples[consptns/@#],UnsameQ@@#&]!={}&]],{n,0,15}]

A387179 Number of twice-partitions of n into distinct constant partitions.

Original entry on oeis.org

1, 1, 2, 4, 7, 11, 18, 28, 48, 69, 105, 158, 240, 343, 503, 720, 1041, 1459, 2062, 2874, 4047, 5547, 7656, 10472, 14322, 19360, 26214, 35192, 47354, 63030, 83992, 111258, 147360, 193804, 254907, 333553, 436319, 567673, 738197, 956049, 1237453, 1594700, 2053361

Offset: 0

Gus Wiseman, Sep 07 2025

A twice-partition of n (A063834) is a sequence of integer partitions, one of each part of an integer partition of n.

			The a(1) = 1 through a(6) = 18 twice-partitions counted by this sequence:
  (1)  (2)   (3)      (4)       (5)         (6)
       (11)  (111)    (22)      (3)(2)      (33)
             (2)(1)   (1111)    (4)(1)      (222)
             (11)(1)  (3)(1)    (11111)     (4)(2)
                      (11)(2)   (22)(1)     (5)(1)
                      (2)(11)   (3)(11)     (22)(2)
                      (111)(1)  (111)(2)    (4)(11)
                                (111)(11)   (111111)
                                (1111)(1)   (111)(3)
                                (11)(2)(1)  (22)(11)
                                (2)(11)(1)  (3)(111)
                                            (1111)(2)
                                            (3)(2)(1)
                                            (1111)(11)
                                            (11111)(1)
                                            (3)(11)(1)
                                            (111)(2)(1)
                                            (111)(11)(1)

Alois P. Heinz, Table of n, a(n) for n = 0..5000

The non-distinct version is A279784.
Dominates the case of distinct block-sums A279786.
This is the constant-block case of A296122.
For strict instead of constant partitions we have A358914.
A000041 counts integer partitions, strict A000009.
A047968 counts constant twice-partitions.
A063834 counts twice-partitions.
Cf. A387120, zeros A387180 (counted by A387329), nonzeros A387181 (counted by A387330).
Cf. A000005, A006906, A007425, A261049, A270995, A299200, A299201, A355739, A387110.

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(j!*
      binomial(numtheory[tau](i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..45);  # Alois P. Heinz, Sep 08 2025

twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn],{ptn,IntegerPartitions[n]}];
Table[Length[Select[twiptn[n],UnsameQ@@#&&And@@SameQ@@@#&]],{n,0,10}]

More terms from Alois P. Heinz, Sep 08 2025

A387576 Numbers k such that it is possible to choose a sequence of distinct integer partitions, one of each prime index of k (with multiplicity).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 89, 90, 91, 93

Offset: 1

Gus Wiseman, Sep 07 2025

First differs from A276078 in having 16807.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
Also numbers with no prime factor prime(x) whose exponent exceeds A000041(x).

			The prime indices of 125 are (3,3,3), and we have choices such as ((3),(1,1,1),(2,1)), so 125 is included.
The terms together with their prime indices begin:
   1: {}
   2: {1}
   3: {2}
   5: {3}
   6: {1,2}
   7: {4}
   9: {2,2}
  10: {1,3}
  11: {5}
  13: {6}
  14: {1,4}
  15: {2,3}
  17: {7}
  18: {1,2,2}

For initial intervals instead of partitions we have A276078, complement A276079.
For divisors instead of partitions we have A368110, counted by A239312.
These are positions of nonzero terms in A387115.
For sets of strict partitions we have A387177, complement A387176.
Integer partitions of this type are counted by A387328.
The complement is A387577, counted by A387134.
A000041 counts integer partitions, strict A000009.
A003963 multiplies together the prime indices of n.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A238873 counts superdiagonal partitions, ranks A387112.
A239312 counts partitions with choosable divisors, strict A387178.
A289509 lists numbers with relatively prime prime indices.
A370320 counts partitions without choosable divisors, strict A387137.
A387118 counts non-superdiagonal partitions, ranks A387113.
Cf. A000720, A052335, A052337, A120383, A335433, A335448, A355740, A367771, A383706, A387110, A387181.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Select[Tuples[IntegerPartitions/@prix[#]],UnsameQ@@#&]!={}&]

cp's OEIS Frontend

A387120 Number of ways to choose a different constant integer partition of each prime index of n.

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A387137 Number of integer partitions of n whose parts do not have choosable sets of strict integer partitions.

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A387176 Numbers whose prime indices do not have choosable sets of strict integer partitions. Zeros of A387115.

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A387177 Numbers whose prime indices have choosable sets of strict integer partitions. Positions of nonzero terms in A387115.

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A387178 Number of integer partitions of n whose parts have choosable sets of strict integer partitions.

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A387180 Numbers of which it is not possible to choose a different constant integer partition of each prime index.

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A387329 Number of integer partitions of n such that it is not possible to choose a different constant integer partition of each part.

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A387330 Number of integer partitions of n such that it is possible to choose a different constant integer partition of each part.

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A387179 Number of twice-partitions of n into distinct constant partitions.

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