A359189 a(n) = Sum_{d|n} d * 3^(n/d-1).
1, 5, 12, 37, 86, 276, 736, 2261, 6597, 19870, 59060, 177780, 531454, 1595816, 4783272, 14353429, 43046738, 129154113, 387420508, 1162301342, 3486786672, 10460471356, 31381059632, 94143540948, 282429536911, 847289672390, 2541865848120, 7625600676808
Offset: 1
Programs
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Mathematica
a[n_] := DivisorSum[n, 3^(n/#-1)*# &]; Array[a, 28] (* Amiram Eldar, Aug 27 2023 *)
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PARI
a(n) = sumdiv(n, d, d*3^(n/d-1));
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-3*x^k))) -
PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, 3^(k-1)*x^k/(1-x^k)^2))
Formula
G.f.: Sum_{k>=1} k * x^k/(1 - 3 * x^k).
G.f.: Sum_{k>=1} 3^(k-1) * x^k/(1 - x^k)^2.