A070537 Numbers k such that the k-th cyclotomic polynomial has more terms than the largest prime factor of k.

1, 15, 21, 30, 33, 35, 39, 42, 45, 51, 55, 57, 60, 63, 65, 66, 69, 70, 75, 77, 78, 84, 85, 87, 90, 91, 93, 95, 99, 102, 105, 110, 111, 114, 115, 117, 119, 120, 123, 126, 129, 130, 132, 133, 135, 138, 140, 141, 143, 145, 147, 150, 153, 154, 155, 156, 159, 161, 165

Offset: 1

Author

Labos Elemer, May 03 2002

Keywords

• nonn

Comments

When (as at k=105) coefficients are not equal to 1 or -1, terms in C[k,x] are counted with multiplicity. This comment was left by the original author, but please see my comment in A070536. - Antti Karttunen, Feb 15 2019

Union of A324110 and A324111. - Antti Karttunen, Feb 15 2019

It appears that except for the initial 1, the terms are products of two or more distinct odd primes. - Enrique Navarrete, Oct 16 2022

Examples

			k=21: Cyclotomic[21,x] = 1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12 has 9 terms while the largest prime factor of 21 is 7; 9 > 7, so 21 is in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A006530, A051664, A070536, A070776 (complement), A324110, A324111.

Programs

PARI

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ After program in A051664
isA070537(n) = (A051664(n) > A006530(n)); \\ Antti Karttunen, Feb 15 2019
for(n=1,165,if(isA070537(n), print1(n,", ")))

Formula

Numbers n satisfying A070536(n) = A051664(n) - A006530(n) > 0.

Extensions

Edited by N. J. A. Sloane, Nov 30 2022