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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!.
2
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
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!.
FORMULA
a(n) = A318574(A325709(n)).
MAPLE
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
MATHEMATICA
Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>k/PrimePi[p]!]], {n, 100}]//Denominator
KEYWORD
nonn,frac,look
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved