A372679 a(n) = phi(15 * n)/8.

1, 1, 3, 2, 5, 3, 6, 4, 9, 5, 10, 6, 12, 6, 15, 8, 16, 9, 18, 10, 18, 10, 22, 12, 25, 12, 27, 12, 28, 15, 30, 16, 30, 16, 30, 18, 36, 18, 36, 20, 40, 18, 42, 20, 45, 22, 46, 24, 42, 25, 48, 24, 52, 27, 50, 24, 54, 28, 58, 30, 60, 30, 54, 32, 60, 30, 66, 32, 66, 30, 70, 36, 72, 36, 75, 36, 60, 36

Offset

1,3

Links

Table of n, a(n) for n=1..78.

Formula

G.f.: Sum_{k>=1} mu(15 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

Multiplicative with a(p^e) = p^e if p = 3 or 5, and (p-1)*p^(e-1) otherwise.

Sum_{k=1..n} a(k) ~ (225/(64*Pi^2)) * n^2. - Amiram Eldar, May 10 2024

Mathematica

a[n_] := EulerPhi[15 * n]/8; Array[a, 100] (* Amiram Eldar, May 10 2024 *)

Prog

(PARI) a(n) = eulerphi(15*n)/8;
(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, moebius(15*k)*x^k/(1-x^k)^2))

Crossrefs

Column k=15 of A372673.

Cf. A008683.

Sequence in context: A225411 A247815 A057953 * A129231 A166477 A124332

Adjacent sequences: A372676 A372677 A372678 * A372680 A372681 A372682

Keyword

nonn,mult,easy

Author

Seiichi Manyama, May 10 2024

Status

approved