A363645 Expansion of Sum_{k>0} x^k/(1 - k*x^k)^4.
1, 5, 11, 29, 36, 109, 85, 297, 256, 801, 287, 2881, 456, 5965, 3766, 17489, 970, 57385, 1331, 125681, 63498, 294933, 2301, 1072865, 24801, 1867009, 1087030, 4942561, 4496, 15697761, 5457, 28721057, 16895770, 63511593, 1404306, 225177013, 9140, 348661477
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(# - 1)*Binomial[# + 2, 3] &]; Array[a, 40] (* Amiram Eldar, Jul 18 2023 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+2, 3));
Formula
a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+2,3).