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A339686 a(n) = Sum_{d|n} 6^(d-1).

%I A339686 #18 Jun 26 2024 02:06:09
%S A339686 1,7,37,223,1297,7819,46657,280159,1679653,10078999,60466177,
%T A339686 362805091,2176782337,13060740679,78364165429,470185264735,
%U A339686 2821109907457,16926661132171,101559956668417,609359750089711,3656158440109669,21936950700844039,131621703842267137
%N A339686 a(n) = Sum_{d|n} 6^(d-1).
%H A339686 Seiichi Manyama, <a href="/A339686/b339686.txt">Table of n, a(n) for n = 1..1000</a>
%F A339686 G.f.: Sum_{k>=1} x^k / (1 - 6*x^k).
%F A339686 G.f.: Sum_{k>=1} 6^(k-1) * x^k / (1 - x^k).
%F A339686 a(n) ~ 6^(n-1). - _Vaclav Kotesovec_, Jun 05 2021
%t A339686 Table[Sum[6^(d - 1), {d, Divisors[n]}], {n, 1, 23}]
%t A339686 nmax = 23; CoefficientList[Series[Sum[x^k/(1 - 6 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A339686 (PARI) a(n) = sumdiv(n, d, 6^(d-1)); \\ _Michel Marcus_, Dec 13 2020
%o A339686 (Magma)
%o A339686 A339686:= func< n | (&+[6^(d-1): d in Divisors(n)]) >;
%o A339686 [A339686(n): n in [1..40]]; // _G. C. Greubel_, Jun 25 2024
%o A339686 (SageMath)
%o A339686 def A339686(n): return sum(6^(k-1) for k in (1..n) if (k).divides(n))
%o A339686 [A339686(n) for n in range(1,41)] # _G. C. Greubel_, Jun 25 2024
%Y A339686 Column 6 of A308813.
%Y A339686 Cf. A000400, A320071.
%Y A339686 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), this sequence (q=6), A339687 (q=7), A339688 (q=8), A339689 (q=9).
%K A339686 nonn
%O A339686 1,2
%A A339686 _Ilya Gutkovskiy_, Dec 12 2020