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A325703
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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!.
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1
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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
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OFFSET
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1,3
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COMMENTS
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Alternatively, if n = prime(i_1) * ... * prime(i_k), then a(n) is the denominator of 1/i_1! + ... + 1/i_k!.
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LINKS
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Table of n, a(n) for n=1..52.
Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums
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FORMULA
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a(n) = A318574(A325709(n)).
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MATHEMATICA
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Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>k/PrimePi[p]!]], {n, 100}]//Denominator
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CROSSREFS
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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
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KEYWORD
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nonn,frac
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AUTHOR
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Gus Wiseman, May 18 2019
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STATUS
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approved
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