A339686 a(n) = Sum_{d|n} 6^(d-1).

1, 7, 37, 223, 1297, 7819, 46657, 280159, 1679653, 10078999, 60466177, 362805091, 2176782337, 13060740679, 78364165429, 470185264735, 2821109907457, 16926661132171, 101559956668417, 609359750089711, 3656158440109669, 21936950700844039, 131621703842267137

Offset: 1

Author

Ilya Gutkovskiy, Dec 12 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Column 6 of A308813.

Cf. A000400, A320071.

Sums of the form Sum_{d|n} q^(d-1): A034729 (q=2), A034730 (q=3), A113999 (q=10), A339684 (q=4), A339685 (q=5), this sequence (q=6), A339687 (q=7), A339688 (q=8), A339689 (q=9).

Programs

Magma

A339686:= func< n | (&+[6^(d-1): d in Divisors(n)]) >;
[A339686(n): n in [1..40]]; // G. C. Greubel, Jun 25 2024

Mathematica

Table[Sum[6^(d - 1), {d, Divisors[n]}], {n, 1, 23}]
nmax = 23; CoefficientList[Series[Sum[x^k/(1 - 6 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = sumdiv(n, d, 6^(d-1)); \\ Michel Marcus, Dec 13 2020

SageMath

def A339686(n): return sum(6^(k-1) for k in (1..n) if (k).divides(n))
[A339686(n) for n in range(1,41)] # G. C. Greubel, Jun 25 2024

Formula

G.f.: Sum_{k>=1} x^k / (1 - 6*x^k).

G.f.: Sum_{k>=1} 6^(k-1) * x^k / (1 - x^k).

a(n) ~ 6^(n-1). - Vaclav Kotesovec, Jun 05 2021