A359102 a(n) = phi(7 * n)/6.

1, 1, 2, 2, 4, 2, 7, 4, 6, 4, 10, 4, 12, 7, 8, 8, 16, 6, 18, 8, 14, 10, 22, 8, 20, 12, 18, 14, 28, 8, 30, 16, 20, 16, 28, 12, 36, 18, 24, 16, 40, 14, 42, 20, 24, 22, 46, 16, 49, 20, 32, 24, 52, 18, 40, 28, 36, 28, 58, 16, 60, 30, 42, 32, 48, 20, 66, 32, 44, 28, 70, 24, 72, 36, 40, 36, 70, 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(7 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).

From Amiram Eldar, Dec 17 2022: (Start)

Multiplicative with a(7^e) = 7^e, and a(p^e) = (p-1)*p^(e-1) if p != 7.

Dirichlet g.f.: zeta(s-1)/(zeta(s)*(1-1/7^s)).

Sum_{k=1..n} a(k) ~ (49/(16*Pi^2)) * n^2. (End)

Mathematica

Array[EulerPhi[7 #]/6 &, 79] (* Michael De Vlieger, Dec 16 2022 *)

Prog

(PARI) a(n) = eulerphi(7*n)/6;
(PARI) my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(7*k)*x^k/(1-x^k)^2))

Crossrefs

Cf. A195459, A359101.

Cf. A008653, A359099.

Sequence in context: A122977 A275870 A321721 * A003980 A286369 A132801

Adjacent sequences: A359099 A359100 A359101 * A359103 A359104 A359105

Keyword

nonn,easy,mult

Author

Seiichi Manyama, Dec 16 2022

Status

approved