A354849 a(n) = (n-1)! * Sum_{d|n} d^(n/d) / (d-1)!.
1, 3, 5, 34, 29, 1626, 727, 99128, 584649, 12353050, 3628811, 4648976652, 479001613, 803709466574, 11133394272015, 391883024332816, 20922789888017, 312756670075449618, 6402373705728019, 148614866400768768020, 2663970255433783296021
Offset: 1
Keywords
Crossrefs
Cf. A087906.
Programs
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Mathematica
a[n_] := (n - 1)! * DivisorSum[n, #^(n/#)/(# - 1)! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
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PARI
a(n) = (n-1)!*sumdiv(n, d, d^(n/d)/(d-1)!);
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k!)))
Formula
E.g.f.: -Sum_{k>0} log(1 - k * x^k)/k!.
If p is prime, a(p) = p + (p-1)!.