A057860 Number of residue classes modulo n which contain only composite numbers.

0, 0, 0, 1, 0, 2, 0, 3, 2, 4, 0, 6, 0, 6, 5, 7, 0, 10, 0, 10, 7, 10, 0, 14, 4, 12, 8, 14, 0, 19, 0, 15, 11, 16, 9, 22, 0, 18, 13, 22, 0, 27, 0, 22, 19, 22, 0, 30, 6, 28, 17, 26, 0, 34, 13, 30, 19, 28, 0, 41, 0, 30, 25, 31, 15, 43, 0, 34, 23

Offset: 1

Author

Henry Bottomley, Sep 08 2000

Keywords

• nonn
• look

Examples

			a(30) = 19 since 30k+m is always composite if m = 0, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27 or 28
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057858.

Programs

Mathematica

Table[n - EulerPhi[n] - PrimeNu[n], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)

PARI

for(n=1,100, print1(n - eulerphi(n) - omega(n), ", ")) \\ G. C. Greubel, May 13 2017

Formula

a(n) = n - A057859(n) = A051953(n) - A001221(n).