A356539 a(n) = Sum_{d|n} d * 3^(n-d).

1, 5, 12, 49, 86, 492, 736, 3977, 8757, 34030, 59060, 384924, 531454, 2672528, 6672552, 26093113, 43046738, 261646137, 387420508, 2181624374, 4682526672, 17435870644, 31381059632, 204908769276, 299863458511, 1412168408630, 3392641222200, 13912336721584

Offset: 1

Author

Seiichi Manyama, Aug 11 2022

Keywords

• nonn

Crossrefs

Cf. A090879, A342675, A356540.

Programs

Mathematica

a[n_] := DivisorSum[n, # * 3^(n - #) &]; Array[a, 30] (* Amiram Eldar, Aug 11 2022 *)

PARI

a(n) = sumdiv(n, d, d*3^(n-d));

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-(3*x)^k)))

Formula

G.f.: Sum_{k>=1} k * x^k/(1 - (3 * x)^k).

If p is prime, a(p) = p + 3^(p-1).