A372672 a(n) = phi(10 * n)/4.

1, 2, 2, 4, 5, 4, 6, 8, 6, 10, 10, 8, 12, 12, 10, 16, 16, 12, 18, 20, 12, 20, 22, 16, 25, 24, 18, 24, 28, 20, 30, 32, 20, 32, 30, 24, 36, 36, 24, 40, 40, 24, 42, 40, 30, 44, 46, 32, 42, 50, 32, 48, 52, 36, 50, 48, 36, 56, 58, 40, 60, 60, 36, 64, 60, 40, 66, 64, 44, 60, 70, 48, 72, 72, 50, 72, 60, 48

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} mu(10 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

Multiplicative with a(p^e) = p^e if p = 2 or 5, and (p-1)*p^(e-1) otherwise.

From Amiram Eldar, Oct 30 2025; (Start)

Dirichlet g.f.: (zeta(s-1)/zeta(s)) * (2^s/(2^s-1)) * (5^s/(5^s-1)).

Sum_{k=1..n} a(k) ~ 25/(6*Pi^2) * n^2. (End)

Mathematica

a[n_] := EulerPhi[10*n]/4; Array[a, 100] (* Amiram Eldar, Oct 30 2025 *)

Prog

(PARI) a(n) = eulerphi(10*n)/4;
(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, moebius(10*k)*x^k/(1-x^k)^2))

Crossrefs

Partial sums gives A372639.

Column k=10 of A372673.

Cf. A000010 (phi), A008683.

Sequence in context: A214793 A199088 A293974 * A395775 A346036 A138557

Adjacent sequences: A372669 A372670 A372671 * A372673 A372674 A372675

Keyword

nonn,easy,mult

Author

Seiichi Manyama, May 10 2024

Status

approved