A339687 a(n) = Sum_{d|n} 7^(d-1).

1, 8, 50, 351, 2402, 16864, 117650, 823894, 5764851, 40356016, 282475250, 1977343950, 13841287202, 96889128064, 678223075300, 4747562333837, 33232930569602, 232630519768872, 1628413597910450, 11398895225729502, 79792266297729700, 558545864365759264

Offset: 1

Author

Ilya Gutkovskiy, Dec 12 2020

Keywords

• nonn

Links

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

Crossrefs

Column 7 of A308813.

Cf. A000420, A320072.

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), A339686 (q=6), this sequence (q=7), A339688 (q=8), A339689 (q=9).

Programs

Magma

A339687:= func< n | (&+[7^(d-1): d in Divisors(n)]) >;
[A339687(n): n in [1..40]]; // G. C. Greubel, Jun 25 2024

Mathematica

Table[Sum[7^(d - 1), {d, Divisors[n]}], {n, 1, 22}]
nmax = 22; CoefficientList[Series[Sum[x^k/(1 - 7 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = sumdiv(n, d, 7^(d-1)); \\ Michel Marcus, Dec 13 2020

SageMath

def A339687(n): return sum(7^(k-1) for k in (1..n) if (k).divides(n))
[A339687(n) for n in range(1,41)] # G. C. Greubel, Jun 25 2024

Formula

G.f.: Sum_{k>=1} x^k / (1 - 7*x^k).

G.f.: Sum_{k>=1} 7^(k-1) * x^k / (1 - x^k).

a(n) ~ 7^(n-1). - Vaclav Kotesovec, Jun 05 2021