A063084 - OEIS

%I #15 Jun 26 2018 04:58:33

%S 0,-1,-1,2,-2,3,-3,4,4,4,-6,5,-7,6,6,6,-10,7,-11,8,8,8,-14,9,9,9,9,9,

%T -19,10,-20,11,11,11,11,11,-25,12,12,12,-28,13,-29,14,14,14,-32,15,15,

%U 15,15,15,-37,16,16,16,16,16,-42,17,-43,18,18,18,18,18,-48,19,19,19,-51,20,-52,21,21,21,21,21,-57,22,22,22,-60,23,23

%N a(n) = pi(n-1)*n - pi(n)*(n-1), where pi() = A000720().

%C To define as positive sequence let C(n)= A062298; f(a) = pi(a) if a is nonprime, f(a)= C(a) if a is prime. - _Daniel Tisdale_, Nov 07 2008

%D G. A. Kudrevatow, (1970): Exercises in Number Theory. Problem 488; page 56; Prosveshenie, Moscow [in Russian].

%H Harry J. Smith, <a href="/A063084/b063084.txt">Table of n, a(n) for n = 1..1000</a>

%e The function is positive for composite and negative for prime numbers. It is zero at n=1.

%o (PARI) a(n)={if(n>1, primepi(n-1)*n - primepi(n)*(n-1), 0)} \\ _Harry J. Smith_, Aug 17 2009

%Y Cf. A000720, A000027, A010051, A061397, A000040, A002808.

%K sign

%O 1,4

%A _Labos Elemer_, Aug 06 2001