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A295505 a(n) = Sum_{d|n} mu(n/d)*4^(d-1). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

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 *)

PROG

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

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.

Sequence in context: A286183 A058748 A049314 * A001655 A058749 A292483

Adjacent sequences:  A295502 A295503 A295504 * A295506 A295507 A295508

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 23 2017

STATUS

approved

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Last modified May 16 18:13 EDT 2021. Contains 343949 sequences. (Running on oeis4.)