A358593 a(n) = n! * Sum_{d|n} d^(n-d) / d!^(n/d).
1, 3, 7, 49, 121, 2701, 5041, 219521, 1587601, 33446701, 39916801, 17731796545, 6227020801, 2879710009177, 98069239768501, 2418218838097921, 355687428096001, 2832293713653708877, 121645100408832001, 2295597943489176040001, 71029619657111138063041
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, #^(n-#) / #!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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PARI
a(n) = n!*sumdiv(n, d, d^(n-d)/d!^(n/d));
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!-(k*x)^k))))
Formula
E.g.f.: Sum_{k>0} x^k / (k! - (k * x)^k).
If p is prime, a(p) = 1 + p! = A038507(p).