|
%I #14 Jun 05 2021 06:25:36
%S 1,10,82,739,6562,59140,531442,4783708,43046803,387427060,3486784402,
%T 31381119478,282429536482,2541866359780,22876792461604,
%U 205891136878357,1853020188851842,16677181742772430,150094635296999122,1350851718060419878,12157665459057460324
%N a(n) = Sum_{d|n} 9^(d-1).
%H Seiichi Manyama, <a href="/A339689/b339689.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Sum_{k>=1} x^k / (1 - 9*x^k).
%F G.f.: Sum_{k>=1} 9^(k-1) * x^k / (1 - x^k).
%F a(n) ~ 9^(n-1). - _Vaclav Kotesovec_, Jun 05 2021
%t Table[Sum[9^(d - 1), {d, Divisors[n]}], {n, 1, 21}]
%t nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 9 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o (PARI) a(n) = sumdiv(n, d, 9^(d-1)); \\ _Michel Marcus_, Dec 13 2020
%Y Column 9 of A308813.
%Y Cf. A001019, A034729, A034730, A113999, A320074, A339684, A339685, A339686, A339687, A339688.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Dec 12 2020
|
