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A070536 Number of terms in n-th cyclotomic polynomial minus largest prime factor of n; a(1)=1 by convention.

%I A070536 #20 Sep 11 2018 17:02:28
%S A070536 1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,4,0,
%T A070536 10,0,0,0,4,0,0,2,0,0,2,0,0,0,0,0,6,0,0,0,6,0,6,0,0,2,0,0,2,0,18,4,0,
%U A070536 0,8,10,0,0,0,0,2,0,20,4,0,0,0,0,0,2,24,0,10,0,0,2,10,0,10,0,12,0,0,0,4,0,0,6,0,0,26
%N A070536 Number of terms in n-th cyclotomic polynomial minus largest prime factor of n; a(1)=1 by convention.
%C A070536 When (as at n=105) coefficients are not equal 1 or -1 then terms in C[n,x] are counted with multiplicity. - This is the comment by the original author. However, the claim contradicts the given formula, as A051664 counts each nonzero coefficient just once, regardless of its value. For the version summing the absolute values of the coefficients (thus "with multiplicity"), see A318886. - _Antti Karttunen_, Sep 10 2018
%H A070536 Antti Karttunen, <a href="/A070536/b070536.txt">Table of n, a(n) for n = 1..65537</a>
%F A070536 a(n) = A051664(n) - A006530(n).
%e A070536 n=21: Cyclotomic[21,x]=1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12 has 9 terms while largest prime factor of 21 is 7
%t A070536 Array[Length@ Cyclotomic[#, x] - FactorInteger[#][[-1, 1]] &, 105] (* _Michael De Vlieger_, Sep 10 2018 *)
%o A070536 (PARI)
%o A070536 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
%o A070536 A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ From A051664
%o A070536 A070536(n) = (A051664(n) - A006530(n)); \\ _Antti Karttunen_, Sep 10 2018
%Y A070536 Cf. A006530, A051664, A070537, A070776.
%Y A070536 Differs from A318886 for the first time at n=105, where a(105) = 26, while A318886(105) = 28.
%K A070536 nonn
%O A070536 1,15
%A A070536 _Labos Elemer_, May 03 2002
%E A070536 Data section extended to 105 terms by _Antti Karttunen_, Sep 10 2018