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%I A339689 #18 Jun 26 2024 02:05:59
%S A339689 1,10,82,739,6562,59140,531442,4783708,43046803,387427060,3486784402,
%T A339689 31381119478,282429536482,2541866359780,22876792461604,
%U A339689 205891136878357,1853020188851842,16677181742772430,150094635296999122,1350851718060419878,12157665459057460324
%N A339689 a(n) = Sum_{d|n} 9^(d-1).
%H A339689 Seiichi Manyama, <a href="/A339689/b339689.txt">Table of n, a(n) for n = 1..1000</a>
%F A339689 G.f.: Sum_{k>=1} x^k / (1 - 9*x^k).
%F A339689 G.f.: Sum_{k>=1} 9^(k-1) * x^k / (1 - x^k).
%F A339689 a(n) ~ 9^(n-1). - _Vaclav Kotesovec_, Jun 05 2021
%t A339689 Table[Sum[9^(d - 1), {d, Divisors[n]}], {n, 1, 21}]
%t A339689 nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 9 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A339689 (PARI) a(n) = sumdiv(n, d, 9^(d-1)); \\ _Michel Marcus_, Dec 13 2020
%o A339689 (Magma)
%o A339689 A339689:= func< n | (&+[9^(d-1): d in Divisors(n)]) >;
%o A339689 [A339689(n): n in [1..40]]; // _G. C. Greubel_, Jun 25 2024
%o A339689 (SageMath)
%o A339689 def A339689(n): return sum(9^(k-1) for k in (1..n) if (k).divides(n))
%o A339689 [A339689(n) for n in range(1,41)] # _G. C. Greubel_, Jun 25 2024
%Y A339689 Column 9 of A308813.
%Y A339689 Cf. A001019, A320074.
%Y A339689 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), A339687 (q=7), A339688 (q=8), this sequence (q=9).
%K A339689 nonn
%O A339689 1,2
%A A339689 _Ilya Gutkovskiy_, Dec 12 2020

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