A050361 -id:A050361 - cp's OEIS frontend

A325837 The number of coreful divisors of n that are exponentially odd numbers (A268335).

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

Offset: 1

Amiram Eldar, Sep 07 2019

First differs from A050361 at n = 64.
From Amiram Eldar, Sep 08 2023: (Start)
The number of exponentially odd divisors of n is A322483(n), and their sum is A033634(n).
A coreful divisor d of a number n is a divisor with the same set of distinct prime factors as n. (End)
Also, the number of divisors of n that are cubefull exponentially odd numbers (A335988). - Amiram Eldar, Feb 11 2024

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A033634, A050361, A065487, A268335, A295316, A335988, A350390.

Cf. A003557, A005361 (number of coreful divisors), A046951, A268335.

fun[p_,e_] := Floor[(e+1)/2]; a[n_] := Times@@(fun@@@FactorInteger[n]); Array[a, 100]

a(n) = vecprod(apply(x -> (x+1)\2, factor(n)[, 2])); \\ Amiram Eldar, Sep 01 2023

Multiplicative with a(p^e) = floor((e+1)/2).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/(p*(p^2-1))) = 1.231291... (A065487). - Amiram Eldar, Sep 10 2022
a(n) = A046951(A350390(n)) (the number of squares dividing the largest exponentially odd divisor of n). - Amiram Eldar, Sep 01 2023
From Amiram Eldar, Sep 08 2023: (Start)
a(n) = A046951(A003557(n)).
Dirichlet g.f.: zeta(s) * zeta(2*s) * Product_{p prime} (1 - 1/p^(2*s) + 1/p^(3*s)). (End)

Name corrected by Amiram Eldar, Sep 08 2023

A356065 Squarefree numbers whose prime indices are all prime-powers.

Original entry on oeis.org

1, 3, 5, 7, 11, 15, 17, 19, 21, 23, 31, 33, 35, 41, 51, 53, 55, 57, 59, 67, 69, 77, 83, 85, 93, 95, 97, 103, 105, 109, 115, 119, 123, 127, 131, 133, 155, 157, 159, 161, 165, 177, 179, 187, 191, 201, 205, 209, 211, 217, 227, 231, 241, 249, 253, 255, 265, 277

Offset: 1

Gus Wiseman, Jul 25 2022

nonn

			105 has prime indices {2,3,4}, all three of which are prime-powers, so 105 is in the sequence.

The multiplicative version (factorizations) is A050361, non-strict A000688.
Heinz numbers of the partitions counted by A054685, with 1's A106244, non-strict A023894, non-strict with 1's A023893.
Counting twice-partitions of this type gives A279786, non-strict A279784.
Counting twice-factorizations gives A295935, non-strict A296131.
These are the odd products of distinct elements of A302493.
Allowing prime index 1 gives A302496, non-strict A302492.
The case of primes (instead of prime-powers) is A302590, non-strict A076610.
These are the squarefree positions of 1's in A355741.
This is the squarefree case of A355743, complement A356066.
A001222 counts prime-power divisors.
A005117 lists the squarefree numbers.
A034699 gives maximal prime-power divisor.
A246655 lists the prime-powers (A000961 includes 1), towers A164336.
A355742 chooses a prime-power divisor of each prime index.
Cf. A001970, A055887, A063834, A302601, A355731, A355744, A356064.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],SquareFreeQ[#]&&And@@PrimePowerQ/@primeMS[#]&]

Intersection of A005117 and A355743.

A381995 Number of ways to partition the prime indices of n into constant blocks with a common sum.

Original entry on oeis.org

1, 1, 1, 2, 1, 0, 1, 2, 2, 0, 1, 1, 1, 0, 0, 3, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 4, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 0

Offset: 1

Gus Wiseman, Mar 19 2025

nonn

Also the number of factorizations of n into prime powers > 1 with equal sums of prime indices.

			The prime indices of 144 are {1,1,1,1,2,2}, with the following 2 multiset partitions into constant blocks with a common sum:
  {{2,2},{1,1,1,1}}
  {{2},{2},{1,1},{1,1}}
so a(144) = 2.

For just constant blocks we have A000688.
Twice-partitions of this type are counted by A279789.
For just a common sum we have A321455.
For distinct instead of equal sums we have A381635.
Positions of 0 are A381871, counted by A381993.
MM-numbers of these multiset partitions are A382215.
A001055 counts factorizations, strict A045778.
A050361 counts factorizations into distinct prime powers.
A055396 gives least prime index, greatest A061395.
A056239 adds up prime indices, row sums of A112798.
A317141 counts coarsenings of prime indices, refinements A300383.
A353864 counts rucksack partitions, ranked by A353866.
Cf. A279784, A295935, A381453 (lower), A381455 (upper).
Cf. A000720, A000961, A001222, A006171, A265947, A381633, A381719.
Cf. A323774, A382076, A382204, A382524, A383014, A383093, A383309.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]& /@ sps[Range[Length[set]]]];
Table[Length[Select[mps[prix[n]], SameQ@@Total/@#&&And@@SameQ@@@#&]],{n,100}]

A323774(n) = Sum_{A056239(k)=n} a(k). Gus Wiseman, Apr 25 2025

A356068 Number of integers ranging from 1 to n that are not prime-powers (1 is not a prime-power).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 42

Offset: 1

Gus Wiseman, Jul 31 2022

nonn

			The a(30) = 14 numbers: 1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30.

The complement is counted by A025528, with 1's A065515.
For primes instead of prime-powers we have A062298, with 1's A065855.
The version treating 1 as a prime-power is A085970.
One more than the partial sums of A143731.
A000688 counts factorizations into prime-powers.
A001222 counts prime-power divisors.
A246655 lists the prime-powers (A000961 includes 1), towers A164336.
Cf. A000720, A023894, A036234, A050361, A054685, A069513, A355743, A356064, A356065, A356066.

Table[Length[Select[Range[n],!PrimePowerQ[#]&]],{n,100}]

a(n) = A085970(n) + 1.

A366902 The number of exponentially evil divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Amiram Eldar, Oct 27 2023

First differs from A050361 at n = 128.
The number of divisors of n that are exponentially evil numbers (A262675), i.e., numbers having only evil (A001969) exponents in their canonical prime factorization.
The sum of these divisors is A366904(n) and the largest of them is A366906(n).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001969, A004709, A050361, A159481, A262675, A366904, A366906.

Similar sequences: A325837, A353898, A365680, A366901.

f[p_, e_] := Floor[e/2] + If[OddQ[e] || OddQ[DigitCount[e + 1, 2, 1]], 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

s(n) = n\2 + (n%2 || hammingweight(n+1)%2); \\ after Charles R Greathouse IV at A159481
a(n) = vecprod(apply(x -> s(x), factor(n)[, 2]));

Multiplicative with a(p^e) = A159481(e).
a(n) >= 1, with equality if and only if n is a cubefree number (A004709).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} Sum_{k>=1} 1/p^A262675(k) = 1.241359937856... .

A382080 Number of ways to partition the prime indices of n into sets with a common sum.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Mar 20 2025

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 A056239.

Also the number of factorizations of n into squarefree numbers > 1 with equal sums of prime indices.

			The prime indices of 900 are {1,1,2,2,3,3}, with the following partitions into sets with a common sum:
  {{1,2,3},{1,2,3}}
  {{3},{3},{1,2},{1,2}}
So a(900) = 2.

For just sets we have A050320, distinct A050326.
Twice-partitions of this type are counted by A279788.
For just a common sum we have A321455.
MM-numbers of these multiset partitions are A326534 /\ A302478.
For distinct instead of equal sums we have A381633.
For constant instead of strict blocks we have A381995.
Positions of 0 are A381719, counted by A381994.
A000688 counts factorizations into prime powers, distinct A050361.
A001055 counts factorizations, strict A045778.
A055396 gives least prime index, greatest A061395.
A056239 adds up prime indices, row sums of A112798.
A317141 counts coarsenings of prime indices, refinements A300383.
Cf. A000720, A000961, A001222, A006171, A279784, A353866, A381635, A381871.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]& /@ sps[Range[Length[set]]]];
Table[Length[Select[mps[prix[n]], SameQ@@Total/@#&&And@@UnsameQ@@@#&]],{n,100}]

A381991 Numbers whose prime indices have a unique multiset partition into constant multisets with distinct sums.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79

Offset: 1

Gus Wiseman, Mar 22 2025

nonn

Also numbers with a unique factorization into prime powers with distinct sums of prime indices.

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 A056239.

			The prime indices of 270 are {1,2,2,2,3}, and there are two multiset partitions into constant multisets with distinct sums: {{1},{2},{3},{2,2}} and {{1},{3},{2,2,2}}, so 270 is not in the sequence.
The prime indices of 300 are {1,1,2,3,3}, of which there are no multiset partitions into constant multisets with distinct sums, so 300 is not in the sequence.
The prime indices of 360 are {1,1,1,2,2,3}, of which there is only one multiset partition into constant multisets with distinct sums: {{1},{1,1},{3},{2,2}}, so 360 is in the sequence.
The terms together with their prime indices begin:
    1: {}
    2: {1}
    3: {2}
    4: {1,1}
    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}
   19: {8}
   20: {1,1,3}
   21: {2,4}
   22: {1,5}
   23: {9}
   24: {1,1,1,2}
   25: {3,3}

For distinct blocks instead of block-sums we have A004709, counted by A000726.
Twice-partitions of this type are counted by A279786.
MM-numbers of these multiset partitions are A326535 /\ A355743.
These are the positions of 1 in A381635.
For no choices we have A381636 (zeros of A381635), counted by A381717.
For strict instead of constant blocks we have A381870, counted by A382079.
Partitions of this type (unique into constant with distinct) are counted by A382301.
Normal multiset partitions of this type are counted by A382203.
A001055 counts multiset partitions, see A317141 (upper), A300383 (lower), A265947.
A055396 gives least prime index, greatest A061395.
A056239 adds up prime indices, row sums of A112798.
Cf. A000688, A000720, A001222, A003963, A005117, A047966, A050361, A293511, A300385, A381716.
Cf. A006171, A279784, A295935.

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

A050363 Number of ordered factorizations into prime powers greater than 1.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 2, 8, 1, 5, 1, 5, 2, 2, 1, 12, 2, 2, 4, 5, 1, 6, 1, 16, 2, 2, 2, 14, 1, 2, 2, 12, 1, 6, 1, 5, 5, 2, 1, 28, 2, 5, 2, 5, 1, 12, 2, 12, 2, 2, 1, 18, 1, 2, 5, 32, 2, 6, 1, 5, 2, 6, 1, 37, 1, 2, 5, 5, 2, 6, 1, 28, 8, 2, 1, 18, 2, 2, 2, 12, 1, 18, 2, 5, 2, 2, 2, 64

Offset: 1

Christian G. Bower, Oct 15 1999

nonn

a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
The Dirichlet inverse is in A010055, turning all but the first element in A010055 negative. - R. J. Mathar, Jul 15 2010
Not multiplicative: a(6) =2 <> a(2)*a(3) = 1*1. - R. J. Mathar, May 25 2017

			From _R. J. Mathar_, May 25 2017: (Start)
a(p^2)  = 2: factorizations p^2, p*p.
a(p^3)  = 4: factorizations p^3, p^2*p, p*p^2, p*p*p.
a(p*q)  = 2: factorizations p*q, q*p.
a(p*q^2)= 5: factorizations p*q^2, q^2*p, p*q*q, q*p*q, q*q*p. (End)

R. J. Mathar, Table of n, a(n) for n = 1..5000

Cf. A000961, A050360, A050361, A050362, A050363, A050364, A076277.

read(transforms) ;
[1,seq(-A010055(n),n=2..100)] ;
DIRICHLETi(%) ; # R. J. Mathar, May 25 2017

Dirichlet g.f.: 1/(1-B(s)) where B(s) is D.g.f. of characteristic function of prime powers >1.
a(p^k) = 2^(k-1).
a(A002110(k)) = k!.
a(n) = A050364(A101296(n)). - R. J. Mathar, May 26 2017
G.f. A(x) satisfies: A(x) = x + Sum_{p prime, k>=1} A(x^(p^k)). - Ilya Gutkovskiy, May 11 2019

A354911 Number of factorizations of n into relatively prime prime-powers.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Jul 25 2022

nonn

			The a(n) factorizations for n = 6, 12, 24, 36, 48, 72, 96:
  2*3  3*4    3*8      4*9      3*16       8*9        3*32
       2*2*3  2*3*4    2*2*9    2*3*8      2*4*9      3*4*8
              2*2*2*3  3*3*4    3*4*4      3*3*8      2*3*16
                       2*2*3*3  2*2*3*4    2*2*2*9    2*2*3*8
                                2*2*2*2*3  2*3*3*4    2*3*4*4
                                           2*2*2*3*3  2*2*2*3*4
                                                      2*2*2*2*2*3

Wikipedia, Coprime integers.

This is the relatively prime case of A000688, partitions A023894.
Positions of 0's are A246655 (A000961 includes 1).
For strict instead of relatively prime we have A050361, partitions A054685.
Positions of 1's are A000469 (A120944 excludes 1).
For pairwise coprime instead of relatively prime we have A143731.
The version for partitions instead of factorizations is A356067.
A000005 counts divisors.
A001055 counts factorizations.
A001221 counts distinct prime divisors, with sum A001414.
A001222 counts prime-power divisors.
A289509 lists numbers whose prime indices are relatively prime.
A295935 counts twice-factorizations with constant blocks (type PPR).
A355743 lists numbers with prime-power prime indices, squarefree A356065.
Cf. A000837, A023893, A076610, A085970, A106244, A279784, A318721, A355737, A355742, A356064, A356066.

ufacs[s_,n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&, Select[ufacs[Select[s,Divisible[n/d,#]&],n/d],Min@@#>=d&]],{d,Select[s,Divisible[n,#]&]}]];
Table[Length[Select[ufacs[Select[Divisors[n],PrimePowerQ[#]&],n],GCD@@#<=1&]],{n,100}]

a(n) = A000688(n) if n is nonprime, otherwise a(n) = 0.

A381637 Number of multisets that can be obtained by taking the sum of each block of a multiset partition of the prime indices of n into blocks with distinct sums.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 4, 1, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 5, 1, 2, 2, 4, 2, 5, 1, 3, 2, 4, 1, 5, 1, 2, 3, 3, 2, 5, 1, 5, 2, 2, 1, 6, 2, 2, 2

Offset: 1

Gus Wiseman, Mar 10 2025

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.

			The prime indices of 84 are {1,1,2,4}, with 7 multiset partitions into blocks with distinct sums:
  {{1,1,2,4}}
  {{1},{1,2,4}}
  {{2},{1,1,4}}
  {{1,1},{2,4}}
  {{1,2},{1,4}}
  {{1},{2},{1,4}}
  {{1},{4},{1,2}}
with block-sums: {8}, {1,7}, {2,6}, {2,6}, {3,5}, {1,2,5}, {1,3,4}, of which 6 are distinct, so a(84) = 6.

Allowing any block-sums gives A317141  (lower A300383), before sums A001055.
Before taking sums we had A321469.
For distinct blocks instead of distinct block-sums we have A381452.
If each block is a set we have A381634 (zeros A381806), before sums A381633.
For equal instead of distinct block-sums we have A381872, before sums A321455.
Other multiset partitions of prime indices:
- For multisets of constant multisets (A000688) see A381455 (upper), A381453 (lower).
- For set multipartitions (A050320) see A381078 (upper), A381454 (lower).
- For sets of constant multisets (A050361) see A381715.
- For sets of constant multisets with distinct sums (A381635) see A381716, A381636.
A003963 gives product of prime indices.
A055396 gives least prime index, greatest A061395.
A056239 adds up prime indices, row sums of A112798.
A265947 counts refinement-ordered pairs of integer partitions.
Cf. A000720, A001222, A001970, A002846, A045778, A066328, A213385, A299200, A299201, A299202, A300385, A317142.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
mps[mset_]:=Union[Sort[Sort/@(#/.x_Integer:>mset[[x]])]&/@sps[Range[Length[mset]]]];
Table[Length[Union[Sort[Total/@#]&/@Select[mps[prix[n]],UnsameQ@@Total/@#&]]],{n,100}]

cp's OEIS Frontend

A325837 The number of coreful divisors of n that are exponentially odd numbers (A268335).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A356065 Squarefree numbers whose prime indices are all prime-powers.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A381995 Number of ways to partition the prime indices of n into constant blocks with a common sum.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

A356068 Number of integers ranging from 1 to n that are not prime-powers (1 is not a prime-power).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A366902 The number of exponentially evil divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A382080 Number of ways to partition the prime indices of n into sets with a common sum.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A381991 Numbers whose prime indices have a unique multiset partition into constant multisets with distinct sums.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A050363 Number of ordered factorizations into prime powers greater than 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple