A352059 a(n) = Sum_{p|n, p prime} (n-1)!/(n/p-1)!.
0, 1, 2, 6, 24, 180, 720, 840, 20160, 378000, 3628800, 6985440, 479001600, 6235669440, 47221574400, 259459200, 20922789888000, 2972883513600, 6402373705728000, 20274518622758400, 1219830034655232000, 51090956251003468800, 1124000727777607680000
Offset: 1
Keywords
Programs
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Mathematica
a[1] = 0; a[n_] := Plus @@ ((n-1)!/(n/FactorInteger[n][[;;,1]] - 1)!); Array[a, 25] (* Amiram Eldar, Mar 02 2022 *)
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PARI
a(n) = my(f=factor(n)); sum(k=1, #f~, (n-1)!/(n/f[k, 1]-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.