A354844 a(n) = n! * Sum_{d|n} (n/d)^d / (d! * (n/d)!).
1, 3, 4, 29, 6, 1027, 8, 26889, 272170, 861851, 12, 515592013, 14, 1530809295, 668366899216, 9382044672017, 18, 1405750464518419, 20, 1393382139935385621, 4274473667143680022, 30537988748467223, 24, 211745638285336995840025
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, (n/#)^#/(#! * (n/#)!) &]; Array[a, 25] (* Amiram Eldar, Jun 08 2022 *)
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PARI
a(n) = n!*sumdiv(n, d, (n/d)^d/(d!*(n/d)!));
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k!)))
Formula
E.g.f.: Sum_{k>0} (exp(k * x^k) - 1)/k!.
If p is prime, a(p) = 1 + p.