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%I #9 Nov 17 2019 09:31:41
%S 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,
%T 1,5,61,5041,5,3,1,40321,361,19,1,37,1,241,7,362881,1,9,1,4,2521,1441,
%U 1,5,7,73,20161,3628801,1,8,1,39916801,25,6,121,181,1
%N 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!.
%C Alternatively, if n = prime(i_1) * ... * prime(i_k), then a(n) is the numerator of 1/i_1! + ... + 1/i_k!.
%H Antti Karttunen, <a href="/A325704/b325704.txt">Table of n, a(n) for n = 1..5000</a>
%H Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%F a(n) = A318573(A325709(n)).
%t Table[Total[Cases[If[n==1,{},FactorInteger[n]],{p_,k_}:>k/PrimePi[p]!]],{n,100}]//Numerator
%o (PARI) A325704(n) = { my(f=factor(n)); numerator(sum(i=1,#f~,f[i, 2]/(primepi(f[i, 1])!))); }; \\ _Antti Karttunen_, Nov 17 2019
%Y Factorial numbers: A000142, A002982, A011371, A022559, A071626, A076934, A108731, A325272, A325508, A325709.
%Y Reciprocal sum: A002966, A316855, A316856, A316857, A318573, A318574, A325618, A325619, A325620, A325621, A325622, A325623, A325624, A325703.
%K nonn,frac
%O 1,4
%A _Gus Wiseman_, May 18 2019
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