A358595 a(n) = n! * Sum_{d|n} d^n / d!^(n/d).
1, 6, 33, 376, 3245, 67716, 828583, 22050176, 420850809, 12580687900, 285351587411, 11736333558720, 302881333613053, 13450914411140584, 463402585399165875, 22345557703564558336, 827240617573764860177, 48442529220731147887020
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!^(n/d));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!-(k*x)^k))))
Formula
E.g.f.: Sum_{k>0} (k * x)^k/(k! - (k * x)^k).
If p is prime, a(p) = p^p + p!.