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

%I #25 Dec 11 2020 03:57:52

%S 1,4,24,120,624,3096,15624,78000,390600,1952496,9765624,48824880,

%T 244140624,1220687496,6103514976,30517500000,152587890624,

%U 762939059400,3814697265624,19073484374880,95367431624976,476837148437496,2384185791015624,11920928906172000

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

%H Seiichi Manyama, <a href="/A295506/b295506.txt">Table of n, a(n) for n = 1..1431</a>

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

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

%t 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 *)

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

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

%Y Column k=5 of A143325.

%Y First differences of A320089.

%Y Cf. A054720.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Nov 23 2017

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)