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A339685 a(n) = Sum_{d|n} 5^(d-1).

%I A339685 #18 Jun 26 2024 02:05:40
%S A339685 1,6,26,131,626,3156,15626,78256,390651,1953756,9765626,48831406,
%T A339685 244140626,1220718756,6103516276,30517656381,152587890626,
%U A339685 762939846906,3814697265626,19073488282006,95367431656276,476837167968756,2384185791015626,11920929003987656
%N A339685 a(n) = Sum_{d|n} 5^(d-1).
%H A339685 Seiichi Manyama, <a href="/A339685/b339685.txt">Table of n, a(n) for n = 1..1000</a>
%F A339685 G.f.: Sum_{k>=1} x^k / (1 - 5*x^k).
%F A339685 G.f.: Sum_{k>=1} 5^(k-1) * x^k / (1 - x^k).
%F A339685 a(n) ~ 5^(n-1). - _Vaclav Kotesovec_, Jun 05 2021
%t A339685 Table[Sum[5^(d - 1), {d, Divisors[n]}], {n, 1, 24}]
%t A339685 nmax = 24; CoefficientList[Series[Sum[x^k/(1 - 5 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A339685 (PARI) a(n) = sumdiv(n, d, 5^(d-1)); \\ _Michel Marcus_, Dec 13 2020
%o A339685 (Magma)
%o A339685 A339685:= func< n | (&+[5^(d-1): d in Divisors(n)]) >;
%o A339685 [A339685(n): n in [1..40]]; // _G. C. Greubel_, Jun 25 2024
%o A339685 (SageMath)
%o A339685 def A339685(n): return sum(5^(k-1) for k in (1..n) if (k).divides(n))
%o A339685 [A339685(n) for n in range(1,41)] # _G. C. Greubel_, Jun 25 2024
%Y A339685 Column 5 of A308813.
%Y A339685 Cf. A000351, A295506.
%Y A339685 Sums of the form Sum_{d|n} q^(d-1): A034729 (q=2), A034730 (q=3), A113999 (q=10), A339684 (q=4), this sequence (q=5), A339686 (q=6), A339687 (q=7), A339688 (q=8), A339689 (q=9).
%K A339685 nonn
%O A339685 1,2
%A A339685 _Ilya Gutkovskiy_, Dec 12 2020