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

2,4

Comments

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

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A356676 A160271 A274912 * A088673 A339662 A336316

Adjacent sequences: A065131 A065132 A065133 * A065135 A065136 A065137

Keyword

nonn

Author

Labos Elemer, Oct 15 2001

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

Status

approved