A352058 a(n) = Sum_{p|n, p prime} n!/(p!*(n/p)!).
0, 1, 1, 6, 1, 120, 1, 840, 10080, 30240, 1, 3659040, 1, 17297280, 3632428800, 259459200, 1, 1490852563200, 1, 845092863014400, 3379030566912000, 28158588057600, 1, 2565331847811532800, 1077167364120207360000, 64764752532480000, 5001134190558105600000
Offset: 1
Keywords
Programs
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Mathematica
a[1] = 0; a[n_] := Plus @@ (n!/((p=FactorInteger[n][[;;,1]])!*(n/p)!)); Array[a, 30] (* Amiram Eldar, Mar 02 2022 *)
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PARI
a(n) = my(f=factor(n)); sum(k=1, #f~, n!/(f[k, 1]!*(n/f[k, 1])!));
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PARI
my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=1, N, isprime(k)*(exp(x^k)-1)/k!))))
Formula
E.g.f.: Sum_{p prime} (exp(x^p) - 1)/p!.
a(n) = 1 if and only if n is prime.