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 A327813 Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(4) (counted with multiplicity). 1
 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, 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, 8, 4, 4, 2, 8, 8, 2, 4, 4, 4, 4, 2, 16, 2, 4, 2, 8, 16, 6, 4, 8, 8, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA 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. EXAMPLE 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: n = 1: x + 1; n = 2: x + 1; n = 3: (x + w)*(x + (w+1)); n = 4: (x + 1)^2; n = 5: x^4 + x^3 + x^2 + x + 1; n = 6: (x + w)*(x + (w+1)); n = 7: (x^3 + x + 1)*(x^3 + x^2 + 1); n = 8: (x + 1)^4; n = 9: (x^3 + w)*(x^3 + (w+1)); n = 10: x^4 + x^3 + x^2 + x + 1. PROG (PARI) a(n) = my(s=n/2^valuation(n, 2)); eulerphi(n)/znorder(Mod(4, s)) CROSSREFS Cf. A000010. Row 3 of A327818. Sequence in context: A083533 A076500 A060594 * A104361 A211449 A086876 Adjacent sequences:  A327810 A327811 A327812 * A327814 A327815 A327816 KEYWORD nonn,easy AUTHOR Jianing Song, Sep 26 2019 STATUS approved

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Last modified June 4 01:32 EDT 2020. Contains 334809 sequences. (Running on oeis4.)