A295505 a(n) = Sum_{d|n} mu(n/d)*4^(d-1).

1, 3, 15, 60, 255, 1005, 4095, 16320, 65520, 261885, 1048575, 4193220, 16777215, 67104765, 268435185, 1073725440, 4294967295, 17179802640, 68719476735, 274877644740, 1099511623665, 4398045462525, 17592186044415, 70368739967040, 281474976710400

Offset: 1

Author

Seiichi Manyama, Nov 23 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1661

Crossrefs

Sum_{d|n} mu(n/d)*k^(d-1): A000740 (k=2), A034741 (k=3), this sequence (k=4), A295506 (k=5).

Column k=4 of A143325.

First differences of A320088.

Cf. A054719.

Programs

Mathematica

Table[Sum[MoebiusMu[n/d]4^(d-1),{d,Divisors[n]}],{n,30}] (* Harvey P. Dale, Nov 08 2020 *)
nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 4*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

PARI

{a(n) = sumdiv(n, d, moebius(n/d)*4^(d-1))}

Formula

a(n) = A054719(n)/4 for n > 0.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 4*x^k). - Ilya Gutkovskiy, Oct 25 2018