cp's OEIS Frontend

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

%I A070537 #27 Nov 30 2022 06:52:40
%S A070537 1,15,21,30,33,35,39,42,45,51,55,57,60,63,65,66,69,70,75,77,78,84,85,
%T A070537 87,90,91,93,95,99,102,105,110,111,114,115,117,119,120,123,126,129,
%U A070537 130,132,133,135,138,140,141,143,145,147,150,153,154,155,156,159,161,165
%N A070537 Numbers k such that the k-th cyclotomic polynomial has more terms than the largest prime factor of k.
%C A070537 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
%C A070537 Union of A324110 and A324111. - _Antti Karttunen_, Feb 15 2019
%C A070537 It appears that except for the initial 1, the terms are products of two or more distinct odd primes. - _Enrique Navarrete_, Oct 16 2022
%H A070537 Antti Karttunen, <a href="/A070537/b070537.txt">Table of n, a(n) for n = 1..10001</a>
%F A070537 Numbers n satisfying A070536(n) = A051664(n) - A006530(n) > 0.
%e A070537 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.
%o A070537 (PARI)
%o A070537 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
%o A070537 A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ After program in A051664
%o A070537 isA070537(n) = (A051664(n) > A006530(n)); \\ _Antti Karttunen_, Feb 15 2019
%o A070537 for(n=1,165,if(isA070537(n), print1(n,", ")))
%Y A070537 Cf. A006530, A051664, A070536, A070776 (complement), A324110, A324111.
%K A070537 nonn
%O A070537 1,2
%A A070537 _Labos Elemer_, May 03 2002
%E A070537 Edited by _N. J. A. Sloane_, Nov 30 2022