cp's OEIS Frontend

A359101 a(n) = phi(5 * n)/4.

%I A359101 #21 Feb 16 2025 08:34:04
%S A359101 1,1,2,2,5,2,6,4,6,5,10,4,12,6,10,8,16,6,18,10,12,10,22,8,25,12,18,12,
%T A359101 28,10,30,16,20,16,30,12,36,18,24,20,40,12,42,20,30,22,46,16,42,25,32,
%U A359101 24,52,18,50,24,36,28,58,20,60,30,36,32,60,20,66,32,44,30,70,24,72,36,50,36,60,24,78
%N A359101 a(n) = phi(5 * n)/4.
%H A359101 Michael De Vlieger, <a href="/A359101/b359101.txt">Table of n, a(n) for n = 1..10000</a>
%H A359101 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusTransform.html">Moebius Transform</a>.
%H A359101 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F A359101 G.f.: -Sum_{k>=1} mu(5 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).
%F A359101 From _Amiram Eldar_, Dec 17 2022: (Start)
%F A359101 Multiplicative with a(5^e) = 5^e, and a(p^e) = (p-1)*p^(e-1) if p != 5.
%F A359101 Dirichlet g.f.: zeta(s-1)/(zeta(s)*(1-1/5^s)).
%F A359101 Sum_{k=1..n} a(k) ~ (25/(8*Pi^2)) * n^2. (End)
%t A359101 Array[EulerPhi[5 #]/4 &, 79] (* _Michael De Vlieger_, Dec 16 2022 *)
%o A359101 (PARI) a(n) = eulerphi(5*n)/4;
%o A359101 (PARI) my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(5*k)*x^k/(1-x^k)^2))
%Y A359101 Cf. A195459, A359102.
%Y A359101 Cf. A008653, A359100.
%K A359101 nonn,easy,mult
%O A359101 1,3
%A A359101 _Seiichi Manyama_, Dec 16 2022