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 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!. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A134460 A130158 A187497 * A104984 A083868 A128199 Adjacent sequences:  A325701 A325702 A325703 * A325705 A325706 A325707 KEYWORD nonn,frac AUTHOR Gus Wiseman, May 18 2019 STATUS approved

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Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)