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A339687 a(n) = Sum_{d|n} 7^(d-1).

%I A339687 #19 Jun 26 2024 02:06:06
%S A339687 1,8,50,351,2402,16864,117650,823894,5764851,40356016,282475250,
%T A339687 1977343950,13841287202,96889128064,678223075300,4747562333837,
%U A339687 33232930569602,232630519768872,1628413597910450,11398895225729502,79792266297729700,558545864365759264
%N A339687 a(n) = Sum_{d|n} 7^(d-1).
%H A339687 Seiichi Manyama, <a href="/A339687/b339687.txt">Table of n, a(n) for n = 1..1000</a>
%F A339687 G.f.: Sum_{k>=1} x^k / (1 - 7*x^k).
%F A339687 G.f.: Sum_{k>=1} 7^(k-1) * x^k / (1 - x^k).
%F A339687 a(n) ~ 7^(n-1). - _Vaclav Kotesovec_, Jun 05 2021
%t A339687 Table[Sum[7^(d - 1), {d, Divisors[n]}], {n, 1, 22}]
%t A339687 nmax = 22; CoefficientList[Series[Sum[x^k/(1 - 7 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A339687 (PARI) a(n) = sumdiv(n, d, 7^(d-1)); \\ _Michel Marcus_, Dec 13 2020
%o A339687 (Magma)
%o A339687 A339687:= func< n | (&+[7^(d-1): d in Divisors(n)]) >;
%o A339687 [A339687(n): n in [1..40]]; // _G. C. Greubel_, Jun 25 2024
%o A339687 (SageMath)
%o A339687 def A339687(n): return sum(7^(k-1) for k in (1..n) if (k).divides(n))
%o A339687 [A339687(n) for n in range(1,41)] # _G. C. Greubel_, Jun 25 2024
%Y A339687 Column 7 of A308813.
%Y A339687 Cf. A000420, A320072.
%Y A339687 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), this sequence (q=7), A339688 (q=8), A339689 (q=9).
%K A339687 nonn
%O A339687 1,2
%A A339687 _Ilya Gutkovskiy_, Dec 12 2020