A086798 - OEIS

%I #23 Mar 15 2023 07:56:35

%S 0,0,0,1,0,0,0,3,4,0,0,2,0,0,2,7,0,4,0,4,4,0,0,6,16,0,16,6,0,2,0,15,6,

%T 0,8,10,0,0,8,12,0,4,0,10,18,0,0,14,36,16,10,12,0,16,24,18,12,0,0,10,

%U 0,0,28,31,18,6,0,16,14,8,0,22,0,0,34,18,30,8,0,28,52,0,0,16,24,0,18,30,0

%N Number of coefficients equal to zero in n-th cyclotomic polynomial.

%D See A051664.

%H Antti Karttunen, <a href="/A086798/b086798.txt">Table of n, a(n) for n = 1..65537</a> (terms 1..1000 from T. D. Noe)

%F From _Benoit Cloitre_, Aug 06 2003: (Start)

%F a(4n+2) = a(2n+1); a(4n) = a(2n) + phi(2n).

%F When p is an odd prime and m integer >= 1: a(p^m) = a(2*p^m) = p^m - p^(m-1) - p + 1. In particular a(p) = a(2p) = 0. (End)

%F a(n) = 1 + phi(n) - A051664(n). - _T. D. Noe_, Aug 08 2003

%t Table[Count[CoefficientList[Cyclotomic[n, x], x], _?(#==0&)], {n, 0, 100}]

%o (PARI) a(n)=sum(k=0,eulerphi(n),if(polcoeff(polcyclo(n),k),0,1))

%o (PARI) A086798(n) = (1 + eulerphi(n) - length(select(x->x!=0, Vec(polcyclo(n))))); \\ _Antti Karttunen_, Sep 21 2018

%Y Cf. A086765, A086780.

%Y Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).

%K nonn

%O 1,8

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003

%E More terms from _Benoit Cloitre_ and _T. D. Noe_, Aug 06 2003