A160759 Integer averages of n values of pi(n^2) for some n, where pi(n) is the number of primes <= n.

0, 1, 2, 3, 201, 235, 265, 431, 1705, 11744, 33946, 622755, 3446493, 8134880, 14287916, 208340425, 223689468

Offset: 1

Author

Daniel Tisdale, May 25 2009

Keywords

• nonn
• more

Comments

For values of n: 1, 2, 3, 4, 62, 68, 73, 97, 213, 624, 1116, 5364, 13350, 21048, 28351, 116151, 120562, ..., . [Robert G. Wilson v, Jun 05 2009]

Crossrefs

Cf. A050248, Integer averages of n primes for some n.

Programs

Mathematica

lst = {}; s = 0; k = 1; While[k < 239600, s = s + PrimePi[k^2]; If[ Mod[s, k] == 0, AppendTo[lst, s/c]]; k++ ]; lst (* Robert G. Wilson v, Jun 05 2009 *)

Formula

1/k*Sum {j=1..k} Pi(j^2) is an integer. [Robert G. Wilson v, Jun 05 2009]

Extensions

More terms from Robert G. Wilson v, Jun 05 2009