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

1,4

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

Formula

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

Mathematica

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

Prog

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

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.

Sequence in context: A130158 A352930 A187497 * A104984 A083868 A128199

Adjacent sequences: A325701 A325702 A325703 * A325705 A325706 A325707

Keyword

nonn,frac

Author

Gus Wiseman, May 18 2019

Status

approved