cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A295506 #25 Dec 11 2020 03:57:52
%S A295506 1,4,24,120,624,3096,15624,78000,390600,1952496,9765624,48824880,
%T A295506 244140624,1220687496,6103514976,30517500000,152587890624,
%U A295506 762939059400,3814697265624,19073484374880,95367431624976,476837148437496,2384185791015624,11920928906172000
%N A295506 a(n) = Sum_{d|n} mu(n/d)*5^(d-1).
%H A295506 Seiichi Manyama, <a href="/A295506/b295506.txt">Table of n, a(n) for n = 1..1431</a>
%F A295506 a(n) = A054720(n)/5 for n > 0.
%F A295506 G.f.: Sum_{k>=1} mu(k)*x^k/(1 - 5*x^k). - _Ilya Gutkovskiy_, Oct 25 2018
%t A295506 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 A295506 (PARI) {a(n) = sumdiv(n, d, moebius(n/d)*5^(d-1))}
%Y A295506 Sum_{d|n} mu(n/d)*k^(d-1): A000740 (k=2), A034741 (k=3), A295505 (k=4), this sequence (k=5).
%Y A295506 Column k=5 of A143325.
%Y A295506 First differences of A320089.
%Y A295506 Cf. A054720.
%K A295506 nonn
%O A295506 1,2
%A A295506 _Seiichi Manyama_, Nov 23 2017