A339689 a(n) = Sum_{d|n} 9^(d-1).

1, 10, 82, 739, 6562, 59140, 531442, 4783708, 43046803, 387427060, 3486784402, 31381119478, 282429536482, 2541866359780, 22876792461604, 205891136878357, 1853020188851842, 16677181742772430, 150094635296999122, 1350851718060419878, 12157665459057460324

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

Crossrefs

Column 9 of A308813.

Cf. A001019, A034729, A034730, A113999, A320074, A339684, A339685, A339686, A339687, A339688.

Sequence in context: A287825 A199701 A103460 * A238843 A360698 A026954

Adjacent sequences: A339686 A339687 A339688 * A339690 A339691 A339692

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 12 2020

Status

approved