cp's OEIS Frontend

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

%I A327812 #6 Sep 28 2019 22:33:55
%S A327812 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,
%T A327812 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,
%U A327812 4,2,2,12,6,2,2,2,2,8,1,8,54,5,2,4,4,1,2,4,1,6
%N A327812 Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(3) (counted with multiplicity).
%F A327812 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.
%e A327812 Factorizations of the n-th cyclotomic polynomial over GF(3) for n <= 10:
%e A327812 n = 1: x - 1;
%e A327812 n = 2: x + 1;
%e A327812 n = 3: (x - 1)^2;
%e A327812 n = 4: x^2 + 1;
%e A327812 n = 5: x^4 + x^3 + x^2 + x + 1;
%e A327812 n = 6: (x + 1)^2;
%e A327812 n = 7: x^6 + x^5 + x^4 + x^3 + x^2 + x + 1;
%e A327812 n = 8: (x^2 + x - 1)*(x^2 - x - 1);
%e A327812 n = 9: (x - 1)^6;
%e A327812 n = 10: x^4 - x^3 + x^2 - x^2 + 1.
%o A327812 (PARI) a(n) = my(s=n/3^valuation(n, 3)); eulerphi(n)/znorder(Mod(3, s))
%Y A327812 Cf. A000010.
%Y A327812 Row 2 of A327818.
%K A327812 nonn,easy
%O A327812 1,3
%A A327812 _Jianing Song_, Sep 26 2019