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A339686 a(n) = Sum_{d|n} 6^(d-1). 8

%I #14 Jun 05 2021 06:23:58

%S 1,7,37,223,1297,7819,46657,280159,1679653,10078999,60466177,

%T 362805091,2176782337,13060740679,78364165429,470185264735,

%U 2821109907457,16926661132171,101559956668417,609359750089711,3656158440109669,21936950700844039,131621703842267137

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

%H Seiichi Manyama, <a href="/A339686/b339686.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum_{k>=1} x^k / (1 - 6*x^k).

%F G.f.: Sum_{k>=1} 6^(k-1) * x^k / (1 - x^k).

%F a(n) ~ 6^(n-1). - _Vaclav Kotesovec_, Jun 05 2021

%t Table[Sum[6^(d - 1), {d, Divisors[n]}], {n, 1, 23}]

%t nmax = 23; CoefficientList[Series[Sum[x^k/(1 - 6 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%o (PARI) a(n) = sumdiv(n, d, 6^(d-1)); \\ _Michel Marcus_, Dec 13 2020

%Y Column 6 of A308813.

%Y Cf. A000400, A034729, A034730, A113999, A320071, A339684, A339685, A339687, A339688, A339689.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 12 2020

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)