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Integer averages of n values of pi(n^2) for some n, where pi(n) is the number of primes <= n.
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%I #10 Mar 15 2015 17:19:15

%S 0,1,2,3,201,235,265,431,1705,11744,33946,622755,3446493,8134880,

%T 14287916,208340425,223689468

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

%C 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]

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

%t 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 *)

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

%K nonn,more

%O 1,3

%A _Daniel Tisdale_, May 25 2009

%E More terms from _Robert G. Wilson v_, Jun 05 2009