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A343574
a(n) = Sum_{d|n} d^d * binomial(d+n/d-1, d).
5
1, 6, 30, 272, 3130, 46794, 823550, 16778544, 387420768, 10000018820, 285311670622, 8916100779324, 302875106592266, 11112006832146486, 437893890380925960, 18446744073860555680, 827240261886336764194, 39346408075300413088392
OFFSET
1,2
FORMULA
G.f.: Sum_{k >= 1} (k * x)^k/(1 - x^k)^(k+1).
If p is prime, a(p) = p + p^p.
MATHEMATICA
a[n_] := DivisorSum[n, #^#*Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Apr 20 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, d^d*binomial(d+n/d-1, d));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^(k+1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 20 2021
STATUS
approved