A359018 a(n) = Sum_{d|n} d * 3^(d-1).

1, 7, 28, 115, 406, 1492, 5104, 17611, 59077, 197242, 649540, 2127364, 6908734, 22325632, 71744968, 229600123, 731794258, 2324583475, 7360989292, 23245426690, 73222477552, 230128420012, 721764371008, 2259438436708, 7060738412431, 22029510754258, 68630377423960

Offset: 1

Author

Seiichi Manyama, Dec 19 2022

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002129, A034730, A083413, A167531, A359186, A359189.

Programs

Magma

A359018:= func< n | (&+[3^(d-1)*d: d in Divisors(n)]) >;
[A359018(n): n in [1..40]]; // G. C. Greubel, Jun 26 2024

Mathematica

a[n_] := DivisorSum[n, 3^(#-1)*# &]; Array[a, 27] (* Amiram Eldar, Aug 27 2023 *)

PARI

a(n) = sumdiv(n, d, d*3^(d-1));

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-3*x^k)^2))

SageMath

def A359018(n): return sum(3^(k-1)*k for k in (1..n) if (k).divides(n))
[A359018(n) for n in range(1,41)] # G. C. Greubel, Jun 26 2024

Formula

G.f.: Sum_{k>=1} x^k/(1 - 3 * x^k)^2.