A295506 a(n) = Sum_{d|n} mu(n/d)*5^(d-1).

1, 4, 24, 120, 624, 3096, 15624, 78000, 390600, 1952496, 9765624, 48824880, 244140624, 1220687496, 6103514976, 30517500000, 152587890624, 762939059400, 3814697265624, 19073484374880, 95367431624976, 476837148437496, 2384185791015624, 11920928906172000

Offset: 1

Author

Seiichi Manyama, Nov 23 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1431

Crossrefs

Sum_{d|n} mu(n/d)*k^(d-1): A000740 (k=2), A034741 (k=3), A295505 (k=4), this sequence (k=5).

Column k=5 of A143325.

First differences of A320089.

Cf. A054720.

Programs

Mathematica

nmax = 20; Rest[CoefficientList[Series[Sum[MoebiusMu[k] * x^k / (1 - 5*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)

PARI

{a(n) = sumdiv(n, d, moebius(n/d)*5^(d-1))}

Formula

a(n) = A054720(n)/5 for n > 0.

G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 5*x^k). - Ilya Gutkovskiy, Oct 25 2018