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A372677
a(n) = phi(13 * n)/12.
1
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
1,3
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
MATHEMATICA
a[n_] := EulerPhi[13 * n]/12; Array[a, 100] (* Amiram Eldar, May 10 2024 *)
PROG
(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))
CROSSREFS
Column k=13 of A372673.
Cf. A008683.
Sequence in context: A293484 A000010 A372681 * A003978 A122645 A372676
KEYWORD
nonn,mult,easy
AUTHOR
Seiichi Manyama, May 10 2024
STATUS
approved