A035470 -id:A035470 - cp's OEIS frontend

A361865 Number of set partitions of {1..n} such that the mean of the means of the blocks is an integer.

1, 0, 3, 2, 12, 18, 101, 232, 1547, 3768, 24974, 116728, 687419, 3489664, 26436217, 159031250, 1129056772

Offset: 1

Gus Wiseman, Apr 04 2023

			The set partition y = {{1,4},{2,5},{3}} has block-means {5/2,7/2,3}, with mean 3, so y is counted under a(5).
The a(1) = 1 through a(5) = 12 set partitions:
  {{1}}  .  {{123}}      {{1}{234}}  {{12345}}
            {{13}{2}}    {{123}{4}}  {{1245}{3}}
            {{1}{2}{3}}              {{135}{24}}
                                     {{15}{234}}
                                     {{1}{234}{5}}
                                     {{12}{3}{45}}
                                     {{135}{2}{4}}
                                     {{14}{25}{3}}
                                     {{15}{24}{3}}
                                     {{1}{24}{3}{5}}
                                     {{15}{2}{3}{4}}
                                     {{1}{2}{3}{4}{5}}

For median instead of mean we have A361864.
For sum instead of outer mean we have A361866, median A361911.
A000110 counts set partitions.
A067538 counts partitions with integer mean, ranks A326836, strict A102627.
A308037 counts set partitions whose block-sizes have integer mean.
A327475 counts subsets with integer mean, median A000975.
Cf. A007837, A035470, A038041, A275714, A275780, A326512, A326513, A326521, A326537, A327481.

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[sps[Range[n]],IntegerQ[Mean[Mean/@#]]&]],{n,6}]

a(13)-a(17) from Christian Sievers, Jun 30 2025

A371788 Triangle read by rows where T(n,k) is the number of set partitions of {1..n} with exactly k distinct block-sums.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 8, 4, 1, 0, 2, 19, 24, 6, 1, 0, 2, 47, 95, 49, 9, 1, 0, 6, 105, 363, 297, 93, 12, 1, 0, 12, 248, 1292, 1660, 753, 158, 16, 1, 0, 11, 563, 4649, 8409, 5591, 1653, 250, 20, 1, 0, 2, 1414, 15976, 41264, 38074, 15590, 3249, 380, 25, 1

Offset: 0

Gus Wiseman, Apr 16 2024

			The set partition {{1,3},{2},{4}} has two distinct block-sums {2,4} so is counted under T(4,2).
Triangle begins:
     1
     0     1
     0     1     1
     0     2     2     1
     0     2     8     4     1
     0     2    19    24     6     1
     0     2    47    95    49     9     1
     0     6   105   363   297    93    12     1
     0    12   248  1292  1660   753   158    16     1
     0    11   563  4649  8409  5591  1653   250    20     1
     0     2  1414 15976 41264 38074 15590  3249   380    25     1
Row n = 4 counts the following set partitions:
  .  {{1,4},{2,3}}  {{1},{2,3,4}}    {{1},{2},{3,4}}  {{1},{2},{3},{4}}
     {{1,2,3,4}}    {{1,2},{3},{4}}  {{1},{2,3},{4}}
                    {{1,2},{3,4}}    {{1},{2,4},{3}}
                    {{1,3},{2},{4}}  {{1,4},{2},{3}}
                    {{1,3},{2,4}}
                    {{1,2,3},{4}}
                    {{1,2,4},{3}}
                    {{1,3,4},{2}}

Row sums are A000110.
Column k = 1 is A035470.
A version for integer partitions is A116608.
For block lengths instead of sums we have A208437.
A008277 counts set partitions by length.
A275780 counts set partitions with distinct block-sums.
A371737 counts quanimous strict partitions, non-strict A321452.
A371789 counts non-quanimous sets, differences A371790.
Cf. A007837, A038041, A327899, A336137, A336138, A365663, A365661, A365925.

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[sps[Range[n]], Length[Union[Total/@#]]==k&]],{n,0,5},{k,0,n}]

A112956 a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 5, 11, 10, 1, 79, 165, 1, 664, 2917, 3308, 9295, 23729, 31874, 301029, 422896, 1, 13716866, 71504979, 100664384, 54148590, 880696661, 498017758, 27450476786, 111911522818, 179459955553, 2144502175213, 59115423982, 45837019664551

Offset: 1

Floor van Lamoen, Oct 07 2005

nonn

For n=7 we have splittings 761/5432, 752/6431, 743/6521, 7421/653 and 7/61/52/43 so a(7)=5.

a(n) = 1 <=> n*(n+1)/2 is product of two primes. - Alois P. Heinz, Sep 03 2009

Cf. A035470.

Cf. A164977, A164978. - Alois P. Heinz, Sep 03 2009

with(numtheory): b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local i, m, x; m:= n*(n+1)/2; add(b(i$(m/i), n)/(m/i)!, i=[select(x-> x>=n, divisors(m) minus {m})[]]) end: seq(a(n), n=1..25);  # Alois P. Heinz, Sep 03 2009

b[args_List] := b[args] = If[args[[1]] == 0, If[Length[args] == 2, 1, b[Rest[args]]], Sum[If[args[[j]] - args[[-1]] < 0, 0, b[Sort[Join[ Table[ args[[i]] - If[i == j, args[[-1]], 0], {i, 1, Length[args] - 1}]]], {args[[-1]] - 1}]], {j, 1, Length[args] - 1}]]; b[a1_List, a2_List] := b[Join[a1, a2]];
a[n_] := a[n] = With[{m = n*(n + 1)/2}, Sum[b[Append[Array[i&, m/i], n]] / (m/i)!, {i, Select[Divisors[m] ~Complement~ {m}, # >= n&]}]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 22 2017, after Alois P. Heinz *)

a(n) = A035470(n) - 1. - Franklin T. Adams-Watters, Jun 02 2006

More terms from Franklin T. Adams-Watters, Jun 02 2006
a(19)-a(33) from Alois P. Heinz, Sep 03 2009
a(34) from Alois P. Heinz, Aug 06 2016

A371734 Maximal length of a factorization of n into factors > 1 all having different sums of prime indices.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 3, 3

Offset: 1

Gus Wiseman, Apr 13 2024

nonn

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. Sum of prime indices is given by A056239.

Factorizations into factors > 1 all having different sums of prime indices are counted by A321469.

			The factorizations of 90 of this type are (2*3*15), (2*5*9), (2*45), (3*30), (5*18), (6*15), (90), so a(90) = 3.

For set partitions of binary indices we have A000120, same sums A371735.
Positions of 1's are A000430.
Positions of terms > 1 are A080257.
Factorizations of this type are counted by A321469, same sums A321455.
For same instead of different sums we have A371733.
A001055 counts factorizations.
A002219 (aerated) counts biquanimous partitions, ranks A357976.
A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
A321451 counts non-quanimous partitions, ranks A321453.
A321452 counts quanimous partitions, ranks A321454.
Cf. A035470, A279787, A305551, A321142, A322794, A326515, A326518, A326534, A336137, A371783, A371789, A371791.

facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&, Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
Table[Max[Length/@Select[facs[n],UnsameQ@@hwt/@#&]],{n,100}]

A056239(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1])));
all_have_different_sum_of_pis(facs) = if(!#facs, 1, (#Set(apply(A056239,facs)) == #facs));
A371734(n, m=n, facs=List([])) = if(1==n, if(all_have_different_sum_of_pis(facs),#facs,0), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs,d); s = max(s,A371734(n/d, d, newfacs)))); (s)); \\ Antti Karttunen, Jan 20 2025

Data section extended to a(105) by Antti Karttunen, Jan 20 2025

A371735 Maximal length of a set partition of the binary indices of n into blocks all having the same sum.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1

Offset: 0

Gus Wiseman, Apr 14 2024

nonn

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

If a(n) = k then the binary indices of n (row n of A048793) are k-quanimous (counted by A371783).

			The binary indices of 119 are {1,2,3,5,6,7}, and the set partitions into blocks with the same sum are:
  {{1,7},{2,6},{3,5}}
  {{1,5,6},{2,3,7}}
  {{1,2,3,6},{5,7}}
  {{1,2,3,5,6,7}}
So a(119) = 3.

Set partitions of this type are counted by A035470, A336137.
A version for factorizations is A371733.
Positions of 1's are A371738.
Positions of terms > 1 are A371784.
A001055 counts factorizations.
A002219 (aerated) counts biquanimous partitions, ranks A357976.
A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
A070939 gives length of binary expansion.
A321452 counts quanimous partitions, ranks A321454.
A326031 gives weight of the set-system with BII-number n.
A371783 counts k-quanimous partitions.
A371789 counts non-quanimous sets, differences A371790.
A371796 counts quanimous sets, differences A371797.
Cf. A006827, A038041, A096111, A279787, A305551, A321451, A321455, A322794, A326534, A371731, A371734.

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
Table[Max[Length/@Select[sps[bix[n]],SameQ@@Total/@#&]],{n,0,100}]

A371839 Number of integer partitions of n with biquanimous multiplicities.

Original entry on oeis.org

1, 0, 0, 1, 1, 2, 3, 4, 6, 9, 11, 16, 22, 29, 38, 52, 66, 88, 114, 147, 186, 245, 302, 389, 486, 613, 757, 960, 1172, 1466, 1790, 2220, 2695, 3332, 4013, 4926, 5938, 7228, 8660, 10519, 12545, 15151, 18041, 21663, 25701, 30774, 36361, 43359, 51149, 60720, 71374

Offset: 0

Gus Wiseman, Apr 18 2024

nonn

A finite multiset of numbers is defined to be biquanimous iff it can be partitioned into two multisets with equal sums. Biquanimous partitions are counted by A002219 and ranked by A357976.

			The partition y = (6,2,1,1) has multiplicities (1,1,2), which are biquanimous because we have the partition ((1,1),(2)), so y is counted under a(10).
The a(0) = 1 through a(10) = 11 partitions:
  ()  .  .  (21)  (31)  (32)  (42)    (43)    (53)    (54)      (64)
                        (41)  (51)    (52)    (62)    (63)      (73)
                              (2211)  (61)    (71)    (72)      (82)
                                      (3211)  (3221)  (81)      (91)
                                              (3311)  (3321)    (3322)
                                              (4211)  (4221)    (4321)
                                                      (4311)    (4411)
                                                      (5211)    (5221)
                                                      (222111)  (5311)
                                                                (6211)
                                                                (322111)

For parts instead of multiplicities we have A002219 aerated, ranks A357976.
These partitions have Heinz numbers A371781.
The complement for parts instead of multiplicities is counted by A371795, ranks A371731, bisections A006827, A058695.
The complement is counted by A371840, ranks A371782.
A237258 = biquanimous strict partitions, ranks A357854, complement A371794.
A321451 counts non-quanimous partitions, ranks A321453.
A321452 counts quanimous partitions, ranks A321454.
A371783 counts k-quanimous partitions.
A371791 counts biquanimous sets, differences A232466.
A371792 counts non-biquanimous sets, differences A371793.
Cf. A035470, A064914, A305551, A321142, A365543, A365925, A367094.

biqQ[y_]:=MemberQ[Total/@Subsets[y],Total[y]/2];
Table[Length[Select[IntegerPartitions[n], biqQ[Length/@Split[#]]&]],{n,0,30}]

A371840 Number of integer partitions of n with non-biquanimous multiplicities.

Original entry on oeis.org

0, 1, 2, 2, 4, 5, 8, 11, 16, 21, 31, 40, 55, 72, 97, 124, 165, 209, 271, 343, 441, 547, 700, 866, 1089, 1345, 1679, 2050, 2546, 3099, 3814, 4622, 5654, 6811, 8297, 9957, 12039, 14409, 17355, 20666, 24793, 29432, 35133, 41598, 49474, 58360, 69197, 81395, 96124

Offset: 0

Gus Wiseman, Apr 18 2024

nonn

A finite multiset of numbers is defined to be biquanimous iff it can be partitioned into two multisets with equal sums. Biquanimous partitions are counted by A002219 and ranked by A357976.

			The partition y = (6,2,1,1) has multiplicities (1,1,2), which are biquanimous because we have the partition ((1,1),(2)), so y is not counted under a(10).
The a(1) = 1 through a(8) = 16 partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (111)  (22)    (221)    (33)      (322)      (44)
                    (211)   (311)    (222)     (331)      (332)
                    (1111)  (2111)   (321)     (421)      (422)
                            (11111)  (411)     (511)      (431)
                                     (3111)    (2221)     (521)
                                     (21111)   (4111)     (611)
                                     (111111)  (22111)    (2222)
                                               (31111)    (5111)
                                               (211111)   (22211)
                                               (1111111)  (32111)
                                                          (41111)
                                                          (221111)
                                                          (311111)
                                                          (2111111)
                                                          (11111111)

The complement for parts is counted by A002219 aerated, ranks A357976.
These partitions have Heinz numbers A371782.
For parts we have A371795, ranks A371731, bisections A006827, A058695.
The complement is counted by A371839, ranks A371781.
A237258 = biquanimous strict partitions, ranks A357854, complement A371794.
A321451 counts non-quanimous partitions, ranks A321453.
A321452 counts quanimous partitions, ranks A321454.
A371783 counts k-quanimous partitions.
A371791 counts biquanimous sets, differences A232466.
A371792 counts non-biquanimous sets, differences A371793.
Cf. A035470, A064914, A305551, A321142, A365543, A365925, A367094.

biqQ[y_]:=MemberQ[Total/@Subsets[y],Total[y]/2];
Table[Length[Select[IntegerPartitions[n], !biqQ[Length/@Split[#]]&]],{n,0,30}]

A371955 Numbers with triquanimous prime indices.

Original entry on oeis.org

8, 27, 36, 48, 64, 125, 150, 180, 200, 216, 240, 288, 320, 343, 384, 441, 490, 512, 567, 588, 630, 700, 729, 756, 784, 810, 840, 900, 972, 1000, 1008, 1080, 1120, 1200, 1296, 1331, 1344, 1440, 1600, 1694, 1728, 1792, 1815, 1920, 2156, 2178, 2197, 2304, 2310

Offset: 1

Gus Wiseman, Apr 19 2024

nonn

A finite multiset of numbers is defined to be triquanimous iff it can be partitioned into three multisets with equal sums.

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 terms together with their prime indices begin:
     8: {1,1,1}
    27: {2,2,2}
    36: {1,1,2,2}
    48: {1,1,1,1,2}
    64: {1,1,1,1,1,1}
   125: {3,3,3}
   150: {1,2,3,3}
   180: {1,1,2,2,3}
   200: {1,1,1,3,3}
   216: {1,1,1,2,2,2}
   240: {1,1,1,1,2,3}
   288: {1,1,1,1,1,2,2}
   320: {1,1,1,1,1,1,3}
   343: {4,4,4}
   384: {1,1,1,1,1,1,1,2}
   441: {2,2,4,4}
   490: {1,3,4,4}
   512: {1,1,1,1,1,1,1,1,1}
   567: {2,2,2,2,4}
   588: {1,1,2,4,4}

Robert Israel, Table of n, a(n) for n = 1..500

These are the Heinz numbers of the partitions counted by A002220.
For biquanimous we have A357976, counted by A002219.
For non-biquanimous we have A371731, counted by A371795, even case A006827.
A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
A237258 (aerated) counts biquanimous strict partitions, ranks A357854.
A371783 counts k-quanimous partitions.
Cf. A000005, A002221, A035470, A064914, A232466, A299701, A321142, A321454, A321455, A326534, A357879, A371781.

tripart:= proc(L) local t,X,Y,n,cons,i,R;
  t:= convert(L,`+`)/3;
  n:= nops(L);
  if not t::integer then return false fi;
  cons:= [add(L[i]*X[i],i=1..n)=t,
          add(L[i]*Y[i],i=1..n)=t,
          seq(X[i] + Y[i] <= 1, i=1..n)];
  R:= traperror(Optimization:-Maximize(0, cons, assume=binary));
  R::list
end proc:
primeindices:= proc(n) local F,t;
  F:= ifactors(n)[2];
  map(t -> numtheory:-pi(t[1])$t[2], F)
end proc:
select(tripart @ primindices, [$2..3000]); # Robert Israel, May 19 2025

hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&, Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
Select[Range[1000],Select[facs[#], Length[#]==3&&SameQ@@hwt/@#&]!={}&]

A327899 Number of set partitions of {1..n} with equal block sizes and equal block sums.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 1, 6, 3, 2, 1, 63, 1, 2, 317, 657, 1, 4333, 1, 9609

Offset: 0

Gus Wiseman, Sep 29 2019

			The a(8) = 6 set partitions:
     {{1,2,3,4,5,6,7,8}}
    {{1,2,7,8},{3,4,5,6}}
    {{1,3,6,8},{2,4,5,7}}
    {{1,4,5,8},{2,3,6,7}}
    {{1,4,6,7},{2,3,5,8}}
  {{1,8},{2,7},{3,6},{4,5}}

Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Set partitions with equal block-sizes are A038041.
Set partitions with equal block-sums are A035470.
Cf. A000110, A000258, A005651, A007837, A008277, A275780, A300335, A319189, A326512, A326513, A326515, A327908.

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[sps[Range[n]],And[SameQ@@Length/@#,SameQ@@Total/@#]&]],{n,0,8}]

A336140 Number of ways to choose a set partition of the parts of a strict integer composition of n.

Original entry on oeis.org

1, 1, 1, 5, 5, 9, 39, 43, 73, 107, 497, 531, 951, 1345, 2125, 8789, 9929, 16953, 24723, 38347, 52717, 219131, 240461, 419715, 600075, 938689, 1278409, 1928453, 6853853, 7815657, 13205247, 19051291, 29325121, 40353995, 60084905, 80722899, 277280079, 312239953

Offset: 0

Gus Wiseman, Jul 16 2020

nonn

A strict composition of n is a finite sequence of distinct positive integers summing to n.

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

Set partitions are A000110.
Strict compositions are A032020.
Set partitions of binary indices are A050315.
Set partitions of strict partitions are A294617.
Cf. A000009, A001055, A008289, A035470, A063834, A072574, A137341, A279375.

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2 b(n$2, 0):
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 30 2020

Table[Sum[BellB[Length[ctn]],{ctn,Join@@Permutations/@Select[ IntegerPartitions[n],UnsameQ@@#&]}],{n,0,10}]
(* Second program: *)
b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0,
     BellB[p]*p!, b[n, i-1, p] + b[n-i, Min[n-i, i-1], p+1]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 40] (* Jean-François Alcover, May 21 2021, after Alois P. Heinz *)

a(n) = Sum_{k = 0..n} A000110(k) * A072574(n,k) = Sum_{k = 0..n} k! * A000110(k) * A008289(n,k).

cp's OEIS Frontend

A361865 Number of set partitions of {1..n} such that the mean of the means of the blocks is an integer.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A371788 Triangle read by rows where T(n,k) is the number of set partitions of {1..n} with exactly k distinct block-sums.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A112956 a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums.

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A371734 Maximal length of a factorization of n into factors > 1 all having different sums of prime indices.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A371735 Maximal length of a set partition of the binary indices of n into blocks all having the same sum.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A371839 Number of integer partitions of n with biquanimous multiplicities.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A371840 Number of integer partitions of n with non-biquanimous multiplicities.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A371955 Numbers with triquanimous prime indices.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A327899 Number of set partitions of {1..n} with equal block sizes and equal block sums.