A359190 a(n) = Sum_{d|n} d * 4^(n/d-1).
1, 6, 19, 76, 261, 1074, 4103, 16536, 65593, 262686, 1048587, 4196644, 16777229, 67117098, 268436319, 1073774896, 4294967313, 17180003478, 68719476755, 274878432636, 1099511640197, 4398048608322, 17592186044439, 70368752620104, 281474976711961, 1125899940397134
Offset: 1
Programs
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Mathematica
a[n_] := DivisorSum[n, 4^(n/#-1)*# &]; Array[a, 26] (* Amiram Eldar, Aug 27 2023 *)
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PARI
a(n) = sumdiv(n, d, d*4^(n/d-1));
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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))
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.