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

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, 28, 10, 30, 16, 20, 16, 30, 12, 36, 18, 24, 20, 40, 12, 42, 20, 30, 22, 46, 16, 42, 25, 32, 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

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Moebius Transform.

Eric Weisstein's World of Mathematics, Totient Function.

Formula

G.f.: -Sum_{k>=1} mu(5 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

From Amiram Eldar, Dec 17 2022: (Start)

Multiplicative with a(5^e) = 5^e, and a(p^e) = (p-1)*p^(e-1) if p != 5.

Dirichlet g.f.: zeta(s-1)/(zeta(s)*(1-1/5^s)).

Sum_{k=1..n} a(k) ~ (25/(8*Pi^2)) * n^2. (End)

Mathematica

Array[EulerPhi[5 #]/4 &, 79] (* Michael De Vlieger, Dec 16 2022 *)

Prog

(PARI) a(n) = eulerphi(5*n)/4;
(PARI) my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(5*k)*x^k/(1-x^k)^2))

Crossrefs

Cf. A195459, A359102.

Cf. A008653, A359100.

Sequence in context: A185291 A018216 A059907 * A024931 A256612 A305797

Adjacent sequences: A359098 A359099 A359100 * A359102 A359103 A359104

Keyword

nonn,easy,mult

Author

Seiichi Manyama, Dec 16 2022

Status

approved