A060304 Number of primes below n^3 does not exceed n times the number of primes below n^2.

0, 0, 3, 6, 15, 19, 37, 47, 69, 82, 113, 139, 180, 216, 244, 300, 381, 423, 486, 553, 638, 726, 820, 887, 1029, 1152, 1256, 1376, 1527, 1659, 1794, 1992, 2156, 2357, 2517, 2739, 2909, 3085, 3365, 3627, 3933, 4200, 4380, 4687, 4960, 5313, 5547, 5917, 6395

Offset: 0

Author

Labos Elemer, Mar 26 2001

Keywords

• nonn

Examples

			n=10, 10*pi(100)=250, pi(1000)=168, a(10)=250-168=82.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• S. Segal, On π(x+y)<=π(x)+π(y), Transactions American Mathematical Society, 104 (1962), 523-527.

Crossrefs

Cf. A060199, A060208, A000720.

Programs

Mathematica

Table[n*PrimePi[n^2]-PrimePi[n^3], {n, 1, 100}]

Formula

a(n) = n*pi(n*n) - pi(n*n*n). - Jonathan Sondow, Feb 17 2014

a(n) = n*A038107(n) - A038098(n). - Michel Marcus, Feb 17 2014