A065134 Remainder when n is divided by the number of primes not exceeding n.

0, 1, 0, 2, 0, 3, 0, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 0, 1, 9, 0, 9, 10, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9, 10, 8, 9, 7, 8, 9, 10, 11, 12, 10, 11, 12, 13, 11, 12, 10, 11, 12, 13, 14, 15, 13, 14, 15, 16, 14, 15, 16, 17, 18, 19, 17, 18, 19

Offset: 2

Author

Labos Elemer, Oct 15 2001

Keywords

• nonn

Comments

Also remainder when the number of nonprimes is divided by the number of primes (not exceeding n).

Examples

			n = 2: Pi[2] = 1,Mod[1,1] = 0, the first term = a(2) = 0; n = 100: Pi[100] = 25, Mod[100,25] = 0 = a(100); n = 20: Pi[20] = 8, Mod[20,8] = 4 = a(20).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000720, A057809, A057810, A000040, A065134, A004648, A062298, A065858-A065864, A065133.

Programs

Mathematica

Table[Last@ QuotientRemainder[n, PrimePi[n]], {n, 2, 91}] (* Michael De Vlieger, Jul 04 2016 *)

PARI

{ for (n=2, 1000, write("b065134.txt", n, " ", n%primepi(n)) ) } \\ Harry J. Smith, Oct 11 2009

Formula

a(n) = n (mod pi(n)).

Extensions

Term a(1) removed so OFFSET changed from 1,5 to 2,4 by Harry J. Smith, Oct 11 2009

Since OFFSET is 2,4; Term a(1) removed and a(91) added by Harry J. Smith, Oct 11 2009