A372677 a(n) = phi(13 * n)/12.

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 13, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 13, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 26, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, 32, 26, 52, 18, 40, 24, 36, 28, 58, 16, 60, 30, 36, 32, 52, 20, 66, 32, 44, 24, 70, 24, 72, 36, 40, 36

Offset: 1

Author

Seiichi Manyama, May 10 2024

Keywords

• nonn
• mult
• easy

Crossrefs

Column k=13 of A372673.

Cf. A008683.

Programs

Mathematica

a[n_] := EulerPhi[13 * n]/12; Array[a, 100] (* Amiram Eldar, May 10 2024 *)

PARI

a(n) = eulerphi(13*n)/12;

PARI

my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(13*k)*x^k/(1-x^k)^2))

Formula

G.f.: -Sum_{k>=1} mu(13 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

Multiplicative with a(13^e) = 13^e, and a(p^e) = (p-1)*p^(e-1) if p != 13.

Sum_{k=1..n} a(k) ~ (169/(56*Pi^2)) * n^2. - Amiram Eldar, May 10 2024