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A342677
a(n) = Sum_{d|n} (n/d)^(n-d+1).
3
1, 5, 28, 265, 3126, 46916, 823544, 16793633, 387422677, 10001953190, 285311670612, 8916464313700, 302875106592254, 11112103714568680, 437893891601739648, 18446779258148749825, 827240261886336764178, 39346424755299348744797, 1978419655660313589123980
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>=1} (k * x)^k/(1 - k^(k-1) * x^k).
If p is prime, a(p) = 1 + p^p.
MATHEMATICA
a[n_] := DivisorSum[n, (n/#)^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Mar 18 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, (n/d)^(n-d+1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k^(k-1)*x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2021
STATUS
approved