

A065134


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


10



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
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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, A065858A065864, A065133.
Sequence in context: A079067 A160271 A274912 * A088673 A236138 A035614
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



