A358280 a(n) = Sum_{d|n} (d-1)!.
1, 2, 3, 8, 25, 124, 721, 5048, 40323, 362906, 3628801, 39916930, 479001601, 6227021522, 87178291227, 1307674373048, 20922789888001, 355687428136444, 6402373705728001, 121645100409194912, 2432902008176640723, 51090942171713068802, 1124000727777607680001
Offset: 1
Programs
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Mathematica
a[n_] := DivisorSum[n, (# - 1)! &]; Array[a, 23] (* Amiram Eldar, Aug 30 2023 *)
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PARI
a(n) = sumdiv(n, d, (d-1)!);
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (k-1)!*x^k/(1-x^k)))
Formula
G.f.: Sum_{k>0} (k-1)! * x^k/(1 - x^k).
If p is prime, a(p) = 1 + (p-1)!.