A325704 If n = prime(i_1)^j_1 * ... * prime(i_k)^j_k, then a(n) is the numerator of the reciprocal factorial sum j_1/i_1! + ... + j_k/i_k!.

0, 1, 1, 2, 1, 3, 1, 3, 1, 7, 1, 5, 1, 25, 2, 4, 1, 2, 1, 13, 13, 121, 1, 7, 1, 721, 3, 49, 1, 5, 1, 5, 61, 5041, 5, 3, 1, 40321, 361, 19, 1, 37, 1, 241, 7, 362881, 1, 9, 1, 4, 2521, 1441, 1, 5, 7, 73, 20161, 3628801, 1, 8, 1, 39916801, 25, 6, 121, 181, 1

Offset: 1

Author

Gus Wiseman, May 18 2019

Keywords

• nonn
• frac

Comments

Alternatively, if n = prime(i_1) * ... * prime(i_k), then a(n) is the numerator of 1/i_1! + ... + 1/i_k!.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5000
• Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to Heinz numbers

Crossrefs

Factorial numbers: A000142, A002982, A011371, A022559, A071626, A076934, A108731, A325272, A325508, A325709.

Reciprocal sum: A002966, A316855, A316856, A316857, A318573, A318574, A325618, A325619, A325620, A325621, A325622, A325623, A325624, A325703.

Programs

Mathematica

Table[Total[Cases[If[n==1,{},FactorInteger[n]],{p_,k_}:>k/PrimePi[p]!]],{n,100}]//Numerator

PARI

A325704(n) = { my(f=factor(n)); numerator(sum(i=1,#f~,f[i, 2]/(primepi(f[i, 1])!))); }; \\ Antti Karttunen, Nov 17 2019

Formula

a(n) = A318573(A325709(n)).