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

1, 9, 65, 521, 4097, 32841, 262145, 2097673, 16777281, 134221833, 1073741825, 8589967945, 68719476737, 549756076041, 4398046515265, 35184374186505, 281474976710657, 2251799830495305, 18014398509481985, 144115188210078217, 1152921504607109185

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Formula

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

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

a(n) ~ 8^(n-1). - Vaclav Kotesovec, Jun 05 2021

Mathematica

Table[Sum[8^(d - 1), {d, Divisors[n]}], {n, 1, 21}]
nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 8 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Prog

(PARI) a(n) = sumdiv(n, d, 8^(d-1)); \\ Michel Marcus, Dec 13 2020

Crossrefs

Column 8 of A308813.

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

Sequence in context: A154996 A128195 A103459 * A100311 A259242 A120286

Adjacent sequences: A339685 A339686 A339687 * A339689 A339690 A339691

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 12 2020

Status

approved