A327812 Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(3) (counted with multiplicity).

1, 1, 2, 1, 1, 2, 1, 2, 6, 1, 2, 2, 4, 1, 2, 2, 1, 6, 1, 2, 2, 2, 2, 4, 1, 4, 18, 2, 1, 2, 1, 2, 4, 1, 2, 6, 2, 1, 8, 4, 5, 2, 1, 2, 6, 2, 2, 4, 1, 1, 2, 4, 1, 18, 2, 4, 2, 1, 2, 4, 6, 1, 6, 2, 4, 4, 3, 2, 4, 2, 2, 12, 6, 2, 2, 2, 2, 8, 1, 8, 54, 5, 2, 4, 4, 1, 2, 4, 1, 6

Offset: 1

Author

Jianing Song, Sep 26 2019

Keywords

• nonn
• easy

Examples

			Factorizations of the n-th cyclotomic polynomial over GF(3) for n <= 10:
n = 1: x - 1;
n = 2: x + 1;
n = 3: (x - 1)^2;
n = 4: x^2 + 1;
n = 5: x^4 + x^3 + x^2 + x + 1;
n = 6: (x + 1)^2;
n = 7: x^6 + x^5 + x^4 + x^3 + x^2 + x + 1;
n = 8: (x^2 + x - 1)*(x^2 - x - 1);
n = 9: (x - 1)^6;
n = 10: x^4 - x^3 + x^2 - x^2 + 1.
		

Crossrefs

Cf. A000010.

Row 2 of A327818.

Programs

PARI

a(n) = my(s=n/3^valuation(n, 3)); eulerphi(n)/znorder(Mod(3, s))

Formula

Let n = 3^e*s, gcd(3,s) = 1, then a(n) = phi(n)/ord(3,s), where phi = A000010, ord(k,s) is the multiplicative order of k modulo s. See A327818 for further information.