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

0,3

References

S. Segal, On Pi(x+y)<=Pi(x)+Pi(y). Transactions American Mathematical Society, 104 (1962), 523-527.

Links

Table of n, a(n) for n=0..57.

Formula

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

Example

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

Crossrefs

Cf. A060199, A060208, A000720.

Sequence in context: A097869 A298079 A295783 * A099577 A268500 A357953

Adjacent sequences: A060300 A060301 A060302 * A060304 A060305 A060306

Keyword

nonn

Author

Labos Elemer, Mar 26 2001

Status

approved