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A339712
a(n) = Sum_{d|n} d^(d+n/d-1) * binomial(d+n/d-2, d-1).
5
1, 5, 28, 273, 3126, 46948, 823544, 16781441, 387421948, 10000078446, 285311670612, 8916102176891, 302875106592254, 11112006865913416, 437893890382064056, 18446744074783625217, 827240261886336764178, 39346408075327954053967, 1978419655660313589123980
OFFSET
1,2
FORMULA
G.f.: Sum_{k >= 1} (k * x/(1 - k * x^k))^k.
If p is prime, a(p) = 1 + p^p.
MATHEMATICA
a[n_] := DivisorSum[n, #^(# + n/# - 1) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 25 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, d^(d+n/d-1)*binomial(d+n/d-2, d-1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x/(1-k*x^k))^k))
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 24 2021
STATUS
approved