A075795 Number of k, 0

0, 0, 1, 1, 3, 3, 5, 4, 6, 7, 9, 8, 11, 11, 12, 11, 15, 14, 17, 16, 18, 19, 21, 19, 22, 23, 23, 24, 27, 26, 29, 26, 30, 31, 32, 31, 35, 35, 36, 35, 39, 38, 41, 40, 41, 43, 45, 42, 46, 46, 48, 48, 51, 49, 52, 51, 54, 55, 57, 55, 59, 59, 59, 57, 62, 62, 65, 64, 66, 66, 69, 66, 71

Offset: 1

Author

Benoit Cloitre, Oct 13 2002

Keywords

• nonn

Comments

a(n) >= A000010(n)-1 since if 2<=kRobert Israel, Jul 24 2016

For n>1 a(n) = number of roots of the n-th polynomial in A275345, equal to 1. - Mats Granvik, Jul 24 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• T. M. Apostol, Resultants of Cyclotomic Polynomials, Proc. Amer. Math. Soc. 24, 457-462, 1970.
• T. M. Apostol, The Resultant of the Cyclotomic Polynomials Fm(ax) and Fn(bx), Math. Comput. 29, 1-6, 1975.
• Eric Weisstein's World of Mathematics, Cyclotomic polynomials.

Crossrefs

Cf. A001222, A054372, A073093.

Programs

Maple

seq(n -numtheory:-bigomega(n)-1, n=1..1000); # Robert Israel, Jul 25 2016

Mathematica

Table[n - PrimeOmega@ n - 1, {n, 73}] (* Michael De Vlieger, Jul 26 2016 *)

PARI

a(n)=sum(k=1,n,if(1-polresultant(polcyclo(n),polcyclo(k)),0,1))

Formula

a(n) = n - A073093(n).

a(n) = n - A001222(n) - 1. - Michel Marcus, Jul 24 2016

Extensions

a(30)=2 and a(31)=6 merged into a(30)=26 by Mats Granvik, Jul 24 2016