A065134 - OEIS

%I #18 Jul 04 2016 13:19:37

%S 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,

%T 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,

%U 11,12,13,11,12,10,11,12,13,14,15,13,14,15,16,14,15,16,17,18,19,17,18,19

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

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

%H Harry J. Smith, <a href="/A065134/b065134.txt">Table of n, a(n) for n = 2..1000</a>

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

%e 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).

%t Table[Last@ QuotientRemainder[n, PrimePi[n]], {n, 2, 91}] (* _Michael De Vlieger_, Jul 04 2016 *)

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

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

%K nonn

%O 2,4

%A _Labos Elemer_, Oct 15 2001

%E Term a(1) removed so OFFSET changed from 1,5 to 2,4 by _Harry J. Smith_, Oct 11 2009

%E Since OFFSET is 2,4; Term a(1) removed and a(91) added by _Harry J. Smith_, Oct 11 2009