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A327814
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Number of irreducible factors in the factorization of the n-th cyclotomic polynomial over GF(5) (counted with multiplicity).
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1
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1, 1, 1, 2, 4, 1, 1, 2, 1, 4, 2, 2, 3, 1, 4, 2, 1, 1, 2, 8, 2, 2, 1, 4, 20, 3, 1, 2, 2, 4, 10, 2, 2, 1, 4, 2, 1, 2, 6, 8, 2, 2, 1, 4, 4, 1, 1, 4, 1, 20, 2, 6, 1, 1, 8, 4, 2, 2, 2, 8, 2, 10, 6, 2, 12, 2, 3, 2, 2, 4, 14, 4, 1, 1, 20, 4, 2, 6, 2, 8, 1, 2, 1, 4, 4, 1, 4, 4, 2, 4
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OFFSET
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1,4
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LINKS
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FORMULA
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Let n = 5^e*s, gcd(5,s) = 1, then a(n) = phi(n)/ord(5,s), where phi = A000010, ord(k,s) is the multiplicative order of k modulo s. See A327818 for further information.
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EXAMPLE
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Factorizations of the n-th cyclotomic polynomial over GF(5) for n <= 10:
n = 1: x - 1;
n = 2: x + 1;
n = 3: x^2 + x + 1;
n = 4: (x + 2)*(x - 2);
n = 5: (x - 1)^4;
n = 6: x^2 - x + 1;
n = 7: x^6 + x^5 + x^4 + x^3 + x^2 + x + 1;
n = 8: (x^2 + 2)*(x^2 - 2);
n = 9: x^6 + x^3 + 1;
n = 10: (x + 1)^4.
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PROG
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(PARI) a(n) = my(s=n/5^valuation(n, 5)); eulerphi(n)/znorder(Mod(5, s))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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