A092502 First derivative of cyclotomic(n,x) evaluated at x=1.

1, 1, 3, 2, 10, 1, 21, 4, 9, 2, 55, 2, 78, 3, 4, 8, 136, 3, 171, 4, 6, 5, 253, 4, 50, 6, 27, 6, 406, 4, 465, 16, 10, 8, 12, 6, 666, 9, 12, 8, 820, 6, 903, 10, 12, 11, 1081, 8, 147, 10, 16, 12, 1378, 9, 20, 12, 18, 14, 1711, 8, 1830, 15, 18, 32, 24, 10, 2211, 16, 22, 12, 2485, 12

Offset

1,3

Links

Indranil Ghosh, Table of n, a(n) for n = 1..5000

Formula

a(n) = (phi(n)/2)*Product_{d|n} d^moebius(n/d), n>1.

a(1) = 1; a(p^e) = p * phi(p^e) / 2 for prime p; otherwise, a(n) = phi(n) / 2. - Álvar Ibeas, Jan 15 2023

Mathematica

Table[If[n>1, (EulerPhi[n]/2) * Product[d^MoebiusMu[n/d], {d, Divisors[n]}], 1], {n , 1, 72}] (* Indranil Ghosh, Mar 16 2017 *)

Prog

(PARI) f(n) = {my(r = 1); fordiv(n, d, r*=d^moebius(n/d)); r};
a(n) = if (n==1, 1, f(n)*eulerphi(n)/2); \\ Indranil Ghosh, Mar 16 2017; edited by Michel Marcus, Jan 16 2023

Crossrefs

Cf. A020500.

Sequence in context: A234748 A156528 A234744 * A292923 A354191 A135515

Adjacent sequences: A092499 A092500 A092501 * A092503 A092504 A092505

Keyword

nonn

Author

Vladeta Jovovic, Apr 05 2004

Status

approved