A339685 a(n) = Sum_{d|n} 5^(d-1).

1, 6, 26, 131, 626, 3156, 15626, 78256, 390651, 1953756, 9765626, 48831406, 244140626, 1220718756, 6103516276, 30517656381, 152587890626, 762939846906, 3814697265626, 19073488282006, 95367431656276, 476837167968756, 2384185791015626, 11920929003987656

Offset: 1

Author

Ilya Gutkovskiy, Dec 12 2020

Keywords

• nonn

Links

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

Crossrefs

Column 5 of A308813.

Cf. A000351, A295506.

Sums of the form Sum_{d|n} q^(d-1): A034729 (q=2), A034730 (q=3), A113999 (q=10), A339684 (q=4), this sequence (q=5), A339686 (q=6), A339687 (q=7), A339688 (q=8), A339689 (q=9).

Programs

Magma

A339685:= func< n | (&+[5^(d-1): d in Divisors(n)]) >;
[A339685(n): n in [1..40]]; // G. C. Greubel, Jun 25 2024

Mathematica

Table[Sum[5^(d - 1), {d, Divisors[n]}], {n, 1, 24}]
nmax = 24; CoefficientList[Series[Sum[x^k/(1 - 5 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = sumdiv(n, d, 5^(d-1)); \\ Michel Marcus, Dec 13 2020

SageMath

def A339685(n): return sum(5^(k-1) for k in (1..n) if (k).divides(n))
[A339685(n) for n in range(1,41)] # G. C. Greubel, Jun 25 2024

Formula

G.f.: Sum_{k>=1} x^k / (1 - 5*x^k).

G.f.: Sum_{k>=1} 5^(k-1) * x^k / (1 - x^k).

a(n) ~ 5^(n-1). - Vaclav Kotesovec, Jun 05 2021