OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: Sum_{k>=1} x^k / (1 - 9*x^k).
G.f.: Sum_{k>=1} 9^(k-1) * x^k / (1 - x^k).
a(n) ~ 9^(n-1). - Vaclav Kotesovec, Jun 05 2021
MATHEMATICA
Table[Sum[9^(d - 1), {d, Divisors[n]}], {n, 1, 21}]
nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 9 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, 9^(d-1)); \\ Michel Marcus, Dec 13 2020
(Magma)
A339689:= func< n | (&+[9^(d-1): d in Divisors(n)]) >;
[A339689(n): n in [1..40]]; // G. C. Greubel, Jun 25 2024
(SageMath)
def A339689(n): return sum(9^(k-1) for k in (1..n) if (k).divides(n))
[A339689(n) for n in range(1, 41)] # G. C. Greubel, Jun 25 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 12 2020
STATUS
approved