A372678 a(n) = phi(14 * n)/6.

1, 2, 2, 4, 4, 4, 7, 8, 6, 8, 10, 8, 12, 14, 8, 16, 16, 12, 18, 16, 14, 20, 22, 16, 20, 24, 18, 28, 28, 16, 30, 32, 20, 32, 28, 24, 36, 36, 24, 32, 40, 28, 42, 40, 24, 44, 46, 32, 49, 40, 32, 48, 52, 36, 40, 56, 36, 56, 58, 32, 60, 60, 42, 64, 48, 40, 66, 64, 44, 56, 70, 48, 72, 72, 40, 72, 70, 48

Offset

1,2

Links

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

Formula

G.f.: Sum_{k>=1} mu(14 * 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 7, and (p-1)*p^(e-1) otherwise.

Sum_{k=1..n} a(k) ~ (49/(12*Pi^2)) * n^2. - Amiram Eldar, May 10 2024

Mathematica

a[n_] := EulerPhi[14 * n]/6; Array[a, 100] (* Amiram Eldar, May 10 2024 *)

Prog

(PARI) a(n) = eulerphi(14*n)/6;
(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, moebius(14*k)*x^k/(1-x^k)^2))

Crossrefs

Column k=14 of A372673.

Cf. A008683.

Sequence in context: A108514 A317419 A364843 * A120456 A367039 A115383

Adjacent sequences: A372675 A372676 A372677 * A372679 A372680 A372681

Keyword

nonn,mult,easy

Author

Seiichi Manyama, May 10 2024

Status

approved