Robert Israel, <a href="/A325703/b325703_1.txt">Table of n, a(n) for n = 1..3168</a>
Robert Israel, <a href="/A325703/b325703_1.txt">Table of n, a(n) for n = 1..3168</a>
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nonn,frac,changed,look
Robert Israel, <a href="/A325703/b325703_1.txt">Table of n, a(n) for n = 1..3168</a>
f:= proc(n) local F, t;
F:= ifactors(n)[2];
denom(add(t[2]/numtheory:-pi(t[1])!, t=F))
end proc:
map(f, [$1..100]); # Robert Israel, Oct 13 2024
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allocated for Gus WisemanIf 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, 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
1,3
Alternatively, if n = prime(i_1) * ... * prime(i_k), then a(n) is the denominator of 1/i_1! + ... + 1/i_k!.
Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>k/PrimePi[p]!]], {n, 100}]//Denominator
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nonn,frac
Gus Wiseman, May 18 2019
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