

A342257


Period of the sequence {gcd(n, Phi_n(a)): a in Z}, where Phi_n is the nth 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
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OFFSET

1,2


COMMENTS

a(n) is the period of the nth column of A342255. See A342255 for more information.


LINKS



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^2a+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^4a^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((p1)%(n/p^L[d, 2])==0, p, 1), 1)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



