A384765 a(n) is the rad(n)-th cyclotomic polynomial evaluated at x = -1.

-2, 0, 1, 0, 1, 3, 1, 0, 1, 5, 1, 3, 1, 7, 1, 0, 1, 3, 1, 5, 1, 11, 1, 3, 1, 13, 1, 7, 1, 1, 1, 0, 1, 17, 1, 3, 1, 19, 1, 5, 1, 1, 1, 11, 1, 23, 1, 3, 1, 5, 1, 13, 1, 3, 1, 7, 1, 29, 1, 1, 1, 31, 1, 0, 1, 1, 1, 17, 1, 1, 1, 3, 1, 37, 1, 19, 1, 1, 1, 5, 1

Offset: 1

Author

Mats Granvik, Jun 09 2025

Keywords

• sign

Comments

The polynomials from A374385 (for n > 1), evaluated at x = -1.

Crossrefs

Cf. A020513, A020500, A374412, A374385, A191898, A023900, A007947, A000079.

Programs

Mathematica

nn = 81; A023900[n_] := Total[Divisors[n]*MoebiusMu[Divisors[n]]]; tt = Table[Simplify@Factor[Sum[A023900[GCD[n, k]]*x^k, {k, 1, n}]/(1 - x^n)], {n, 1, nn}];
Denominator[tt] /. {x -> -1}

Formula

a(n) = A020513(A007947(n)). - Andrei Zabolotskii, Jul 21 2025