

A342256


Numbers k such that gcd(k, Phi_k(a)) > 1 for some a, where Phi_k is the kth cyclotomic polynomial.


3



2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 32, 34, 37, 38, 39, 41, 42, 43, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 78, 79, 81, 82, 83, 86, 89, 93, 94, 97, 98, 100, 101
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OFFSET

1,1


COMMENTS

Indices of columns of A342255 with some elements greater than 1.
For k > 1, let p be the largest prime factor of k, then k is a term if and only if k = p^e*d with d  (p1). See A342255 for more information.
Also numbers k such that A342257(k) > 1.


LINKS



FORMULA

Equals Union_{p prime} (Union_{d(p1)} {d*p, d*p^2, ..., d*p^e, ...}).


EXAMPLE

6 is a term since gcd(6, Phi_6(2)) = gcd(6, 3) = 3 > 1.
55 is a term since 55 = 11*5, 5  (111). Indeed, gcd(55, Phi_55(3)) = gcd(55, 8138648440293876241) = 11 > 1.
12 is not a term since 12 = 3*4 but 4 does not divide 31. Indeed, gcd(12, Phi_12(a)) = gcd(12, a^4a^2+1) = 1 for all a.


PROG

(PARI) isA342256(k) = if(k>1, my(L=factor(k), d=omega(k), p=L[d, 1]); (p1)%(k/p^L[d, 2])==0, 0)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



