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A339688 a(n) = Sum_{d|n} 8^(d-1). 8

%I #15 Jun 05 2021 06:25:00

%S 1,9,65,521,4097,32841,262145,2097673,16777281,134221833,1073741825,

%T 8589967945,68719476737,549756076041,4398046515265,35184374186505,

%U 281474976710657,2251799830495305,18014398509481985,144115188210078217,1152921504607109185

%N a(n) = Sum_{d|n} 8^(d-1).

%H Seiichi Manyama, <a href="/A339688/b339688.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum_{k>=1} x^k / (1 - 8*x^k).

%F G.f.: Sum_{k>=1} 8^(k-1) * x^k / (1 - x^k).

%F a(n) ~ 8^(n-1). - _Vaclav Kotesovec_, Jun 05 2021

%t Table[Sum[8^(d - 1), {d, Divisors[n]}], {n, 1, 21}]

%t nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 8 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%o (PARI) a(n) = sumdiv(n, d, 8^(d-1)); \\ _Michel Marcus_, Dec 13 2020

%Y Column 8 of A308813.

%Y Cf. A001018, A034729, A034730, A113999, A320073, A339684, A339685, A339686, A339687, A339689.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 12 2020

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)