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A354845
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a(n) = n! * Sum_{d|n} (n/d)^(d-1) / d!.
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6
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1, 3, 7, 49, 121, 2281, 5041, 134401, 907201, 13184641, 39916801, 3753509761, 6227020801, 393409336321, 7638997766401, 160474477363201, 355687428096001, 75792615407308801, 121645100408832001, 32459310892353945601, 475723576423839744001, 7306033564948620902401
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f.: Sum_{k>0} (exp(k * x^k) - 1)/k.
If p is prime, a(p) = 1 + p!.
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MATHEMATICA
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a[n_] := n! * DivisorSum[n, (n/#)^(#-1)/#! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
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PROG
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(PARI) a(n) = n!*sumdiv(n, d, (n/d)^(d-1)/d!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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