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%I #6 Sep 28 2019 22:34:05
%S 1,1,2,2,2,2,2,4,2,2,2,4,2,2,4,8,4,2,2,4,4,2,2,8,2,2,2,4,2,4,6,16,4,4,
%T 4,4,2,2,4,8,4,4,6,4,4,2,2,16,2,2,8,4,2,2,4,8,4,2,2,8,2,6,12,32,8,4,2,
%U 8,4,4,2,8,8,2,4,4,4,4,2,16,2,4,2,8,16,6,4,8,8,4
%N Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(4) (counted with multiplicity).
%F Let n = 2^e*s, gcd(2,s) = 1, then a(n) = phi(n)/ord(4,s), where phi = A000010, ord(k,s) is the multiplicative order of k modulo s. See A327818 for further information.
%e Let GF(4) = GF(2)[w], where w^2 + w + 1 = 0. Factorizations of the n-th cyclotomic polynomial over GF(4) for n <= 10:
%e n = 1: x + 1;
%e n = 2: x + 1;
%e n = 3: (x + w)*(x + (w+1));
%e n = 4: (x + 1)^2;
%e n = 5: x^4 + x^3 + x^2 + x + 1;
%e n = 6: (x + w)*(x + (w+1));
%e n = 7: (x^3 + x + 1)*(x^3 + x^2 + 1);
%e n = 8: (x + 1)^4;
%e n = 9: (x^3 + w)*(x^3 + (w+1));
%e n = 10: x^4 + x^3 + x^2 + x + 1.
%o (PARI) a(n) = my(s=n/2^valuation(n, 2)); eulerphi(n)/znorder(Mod(4, s))
%Y Cf. A000010.
%Y Row 3 of A327818.
%K nonn,easy
%O 1,3
%A _Jianing Song_, Sep 26 2019
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