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

1,9

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A244234 A237449 A003869 * A120205 A257291 A152465

Adjacent sequences: A065861 A065862 A065863 * A065865 A065866 A065867

Keyword

nonn

Author

Labos Elemer, Nov 26 2001

Status

approved