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A325703 If n = prime(i_1)^j_1 * ... * prime(i_k)^j_k, then a(n) is the denominator of the reciprocal factorial sum j_1/i_1! + ... + j_k/i_k!. 1
1, 1, 2, 1, 6, 2, 24, 1, 1, 6, 120, 2, 720, 24, 3, 1, 5040, 1, 40320, 6, 24, 120, 362880, 2, 3, 720, 2, 24, 3628800, 3, 39916800, 1, 120, 5040, 24, 1, 479001600, 40320, 720, 6, 6227020800, 24, 87178291200, 120, 6, 362880, 1307674368000, 2, 12, 3, 5040, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..52.

Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums

FORMULA

a(n) = A318574(A325709(n)).

MATHEMATICA

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

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, A325704.

Sequence in context: A089849 A185330 A217955 * A321898 A284434 A306543

Adjacent sequences:  A325700 A325701 A325702 * A325704 A325705 A325706

KEYWORD

nonn,frac

AUTHOR

Gus Wiseman, May 18 2019

STATUS

approved

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Last modified March 7 19:13 EST 2021. Contains 341928 sequences. (Running on oeis4.)