A063084 a(n) = pi(n-1)*n - pi(n)*(n-1), where pi() = A000720().

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

Offset: 1

Author

Labos Elemer, Aug 06 2001

Keywords

• sign

Comments

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

Examples

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

References

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

Links

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

Crossrefs

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

Programs

PARI

a(n)={if(n>1, primepi(n-1)*n - primepi(n)*(n-1), 0)} \\ Harry J. Smith, Aug 17 2009