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 A342257 Period of the sequence {gcd(n, Phi_n(a)): a in Z}, where Phi_n is the n-th cyclotomic polynomial. 3
 1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 1, 13, 7, 1, 2, 17, 3, 19, 5, 7, 11, 23, 1, 5, 13, 3, 1, 29, 1, 31, 2, 1, 17, 1, 1, 37, 19, 13, 1, 41, 7, 43, 1, 1, 23, 47, 1, 7, 5, 1, 13, 53, 3, 11, 1, 19, 29, 59, 1, 61, 31, 1, 2, 1, 1, 67, 17, 1, 1, 71, 1, 73, 37, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the period of the n-th column of A342255. See A342255 for more information. Also a(n) is the maximum value of the n-th column of A342255. - Jianing Song, Aug 09 2022 LINKS Jianing Song, Table of n, a(n) for n = 1..10000 FORMULA a(n) is the largest prime factor of n if n is in A342256, 1 otherwise. EXAMPLE gcd(6, Phi_6(a)) = gcd(6, a^2-a+1) = 3 for a == 2 (mod 3), 1 otherwise, so {gcd(6, Phi_6(a)): a in Z} has period 3, hence a(6) = 3. gcd(12, Phi_12(a)) = gcd(12, a^4-a^2+1) = 1 for all n, so {gcd(12, Phi_12(a)): a in Z} has period 1, hence a(12) = 1. PROG (PARI) a(n) = if(n>1, my(L=factor(n), d=omega(n), p=L[d, 1]); if((p-1)%(n/p^L[d, 2])==0, p, 1), 1) CROSSREFS Cf. A342255, A253235 (indices of 1), A342256 (indices of terms other than 1), A006530, A013595 (coefficients of cyclotomic polynomials). Sequence in context: A262549 A086287 A253236 * A286516 A273289 A361725 Adjacent sequences: A342254 A342255 A342256 * A342258 A342259 A342260 KEYWORD nonn,easy AUTHOR Jianing Song, Mar 07 2021 STATUS approved

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Last modified October 2 21:26 EDT 2023. Contains 365840 sequences. (Running on oeis4.)