A057859 Number of residue classes modulo n which contain a prime.

1, 2, 3, 3, 5, 4, 7, 5, 7, 6, 11, 6, 13, 8, 10, 9, 17, 8, 19, 10, 14, 12, 23, 10, 21, 14, 19, 14, 29, 11, 31, 17, 22, 18, 26, 14, 37, 20, 26, 18, 41, 15, 43, 22, 26, 24, 47, 18, 43, 22, 34, 26, 53, 20, 42, 26, 38, 30, 59, 19, 61, 32, 38, 33, 50, 23, 67, 34, 46

Offset: 1

Author

Henry Bottomley, Sep 08 2000

Keywords

• nonn
• look

Comments

a(n) = n iff n is prime; a(2*n)<=n+1; a(4*p)=2*p for primes p>2: a(A001749(n))=A057860(A001749(n)). - Reinhard Zumkeller, Jan 11 2004

Examples

			a(30) = 11 since 30k+m can be prime if m = 2, 3 or 5 (once each with k = 0) or m = 1, 7, 11, 13, 17, 19, 23 or 29 (each for an infinite number of values of k).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057857, A179179.

Programs

Maple

with(numtheory):
a:= n-> phi(n)+nops(factorset(n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 14 2016

Mathematica

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

PARI

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

Formula

a(n) = A000010(n) + A001221(n) = n - A057860(n).