A360794 Expansion of Sum_{k>0} x^k / (1 - k * x^k)^(k+1).
1, 3, 4, 11, 6, 43, 8, 109, 100, 281, 12, 1507, 14, 1863, 3376, 6937, 18, 26245, 20, 53211, 63022, 67739, 24, 572413, 78776, 372945, 1087048, 1761719, 30, 7362871, 32, 9947953, 16897486, 10027349, 8011116, 123101515, 38, 49807779, 241823440, 361722421, 42
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, #^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* Amiram Eldar, Jul 31 2023 *)
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PARI
my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-k*x^k)^(k+1))) -
PARI
a(n) = sumdiv(n, d, d^(n/d-1)*binomial(d+n/d-1, d));
Formula
a(n) = Sum_{d|n} d^(n/d-1) * binomial(d+n/d-1,d).
If p is prime, a(p) = 1 + p.