A060303 Number of primes below n^2 does not exceed n times the number of primes below n.

0, 0, 2, 2, 6, 7, 13, 14, 14, 15, 25, 26, 39, 40, 42, 42, 58, 60, 80, 82, 83, 84, 108, 111, 111, 112, 114, 115, 144, 146, 179, 180, 182, 183, 185, 186, 225, 228, 228, 229, 270, 272, 319, 321, 324, 325, 376, 378, 378, 383, 387, 387, 439, 443, 446, 451, 455, 454

Offset: 1

Author

Labos Elemer, Mar 26 2001

Keywords

• nonn

Examples

			pi(100) = 25, 10*pi(10) = 40, a(10) = 40-25 = 15.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Sanford L. Segal, On Pi(x+y)<=Pi(x)+Pi(y), Transactions American Mathematical Society, Vol. 104, No. 3 (1962), pp. 523-527.

Crossrefs

Cf. A000720, A060199, A060208.

Formula

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

Extensions

Offset corrected by Amiram Eldar, Sep 06 2024