A065864 Remainder when n is divided by the number of nonprimes not exceeding n.

0, 0, 0, 0, 1, 0, 1, 0, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 21

Offset: 1

Author

Labos Elemer, Nov 26 2001

Keywords

• nonn

Examples

			For n=100, pi(100)=25, so a(100) = 100 mod (100-25) = 25.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A004648, A062298, A065133, A065134, A065858-A065864.

Programs

Mathematica

Table[Mod[n, n - PrimePi@ n], {n, 78}] (* or *)
Table[Mod[n, Count[Range@ n, k_ /; ! PrimeQ@ k]], {n, 78}] (* Michael De Vlieger, Jan 01 2017 *)

PARI

{ for (n = 1, 1000, a=n%(n - primepi(n)); write("b065864.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 02 2009

Formula

a(n) = n mod (n-pi(n)) = n mod (n-A000720(n)) = n mod A062298(n).