A070776 Numbers k such that number of terms in the k-th cyclotomic polynomial is equal to the largest prime factor of k.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 64, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 94, 96, 97, 98, 100

Offset: 1

Author

Labos Elemer, May 07 2002

Keywords

• nonn
• easy

Comments

Numbers k such that A051664(k) = A006530(k).

This is also numbers in the form of 2^i*p^j, i >= 0 and j >= 0, p is an odd prime number. - Lei Zhou, Feb 18 2012

From Zhou's formulation (where the exponents i and j should actually have been specified as i > 0 OR j > 0, to exclude 1) it follows that this is a subsequence of A324109. It also follows that A005940(a(n)) = A324106(a(n)) for all n >= 1. - Antti Karttunen, Feb 15 2019

Also from Zhou's formulation, the union (disjoint) of A000079\{1} and A336101. - Peter Munn, Jul 16 2020

Numbers k>=2 such that A078701(k) = A299766(k). - Juri-Stepan Gerasimov, Jun 02 2021

Examples

			n=10: Cyclotomic[10,x]=1-x+x^2-x^3+x^4 with 5 terms [including 1] which equals largest prime factor (5) of 10=n.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of zeros in A070536.

Cf. A005940, A006530, A051664, A061345, A070537 (complement), A324106, A324111.

Subsequence of A324109.

Subsequences: A000079\{1}, A336101.

Programs

Mathematica

Select[Range[1000],(a=FactorInteger[#];b=Length[a];(b==1)||((b==2)&&(a[[1]][[1]]==2)))&] (* Lei Zhou, Feb 18 2012 *)

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
A070536(n) = (A051664(n) - A006530(n));
isA070776(n) = (!A070536(n)); \\ Antti Karttunen, Feb 15 2019
k=0; n=0; while(k<10000, n++; if(isA070776(n), k++; write("b070776.txt", k, " ", n)));