cp's OEIS Frontend

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

%I A070776 #60 Jun 02 2021 22:39:22
%S A070776 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,
%T A070776 29,31,32,34,36,37,38,40,41,43,44,46,47,48,49,50,52,53,54,56,58,59,61,
%U A070776 62,64,67,68,71,72,73,74,76,79,80,81,82,83,86,88,89,92,94,96,97,98,100
%N A070776 Numbers k such that number of terms in the k-th cyclotomic polynomial is equal to the largest prime factor of k.
%C A070776 Numbers k such that A051664(k) = A006530(k).
%C A070776 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
%C A070776 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
%C A070776 Also from Zhou's formulation, the union (disjoint) of A000079\{1} and A336101. - _Peter Munn_, Jul 16 2020
%C A070776 Numbers k>=2 such that A078701(k) = A299766(k). - _Juri-Stepan Gerasimov_, Jun 02 2021
%H A070776 Antti Karttunen, <a href="/A070776/b070776.txt">Table of n, a(n) for n = 1..10000</a>
%e A070776 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.
%t A070776 Select[Range[1000],(a=FactorInteger[#];b=Length[a];(b==1)||((b==2)&&(a[[1]][[1]]==2)))&] (* _Lei Zhou_, Feb 18 2012 *)
%o A070776 (PARI)
%o A070776 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
%o A070776 A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ After program in A051664
%o A070776 A070536(n) = (A051664(n) - A006530(n));
%o A070776 isA070776(n) = (!A070536(n)); \\ _Antti Karttunen_, Feb 15 2019
%o A070776 k=0; n=0; while(k<10000, n++; if(isA070776(n), k++; write("b070776.txt", k, " ", n)));
%Y A070776 Positions of zeros in A070536.
%Y A070776 Cf. A005940, A006530, A051664, A061345, A070537 (complement), A324106, A324111.
%Y A070776 Subsequence of A324109.
%Y A070776 Subsequences: A000079\{1}, A336101.
%K A070776 nonn,easy
%O A070776 1,1
%A A070776 _Labos Elemer_, May 07 2002