OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} k * x^k/(1 - 4 * x^k).
G.f.: Sum_{k>=1} 4^(k-1) * x^k/(1 - x^k)^2.
MATHEMATICA
a[n_] := DivisorSum[n, 4^(n/#-1)*# &]; Array[a, 26] (* Amiram Eldar, Aug 27 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d*4^(n/d-1));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-4*x^k)))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, 4^(k-1)*x^k/(1-x^k)^2))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 19 2022
STATUS
approved