A338658 a(n) = Sum_{d|n} d * binomial(d+n/d-1, d).

1, 4, 6, 14, 10, 36, 14, 56, 48, 80, 22, 228, 26, 140, 240, 316, 34, 552, 38, 820, 546, 308, 46, 2088, 680, 416, 1044, 2156, 58, 4380, 62, 3248, 1782, 680, 4690, 9672, 74, 836, 2808, 14560, 82, 15456, 86, 9108, 17040, 1196, 94, 37704, 12110, 21420, 5916, 16068, 106, 44496

Offset: 1

Author

Seiichi Manyama, Apr 22 2021

Keywords

• nonn

Crossrefs

Cf. A081543, A343574.

Programs

Mathematica

a[n_] := DivisorSum[n, # * Binomial[# + n/# - 1, #] &]; Array[a, 100] (* Amiram Eldar, Apr 22 2021 *)

PARI

a(n) = sumdiv(n, d, d*binomial(d+n/d-1, d));

PARI

my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-x^k)^(k+1)))

Formula

G.f.: Sum_{k >= 1} k * x^k/(1 - x^k)^(k+1).

If p is prime, a(p) = 2*p.