%I #22 Dec 29 2024 18:40:49
%S 1,3,5,10,2640,8304,11699,15330,16810,16910,22463,25906,26652,35950,
%T 72429,75470,134141,142413,194711,270353,296073,371964,496254,654609,
%U 1640679,1729409,1854680,4434965,4973898,5584120,5783816
%N Numbers n such that pi(n^2) is a square.
%C a(28) > 2*10^6. [_Donovan Johnson_, May 30 2010]
%e n = 14: a(14) = 35950, Pi(35950^2) = Pi(1292402500) = 64866916 = 8054^2
%t Do[ If[ IntegerQ[ Sqrt[ PrimePi[n^2]]], Print[n]], {n, 1, 400000} ]
%t lst = {}; Do[ If[ IntegerQ@ Sqrt@ PrimePi[n^2], AppendTo[lst, n]; Print@n], {n, 520000}]; lst (* _Robert G. Wilson v_, Feb 03 2006 *)
%o (PARI) pi(x, c=0) = forprime(p=2,x,c++); c
%o for(n=1,10^6, if(issquare(pi(n^2)),print1(n," ")))
%Y Cf. A000720, A115835 (square root of pi(a(n))).
%K nonn
%O 1,2
%A _Jason Earls_, Oct 07 2001
%E More terms from _Robert G. Wilson v_ and _Labos Elemer_, Oct 08 2001
%E Further terms from _Robert G. Wilson v_, Oct 16 2001
%E a(20) from _Robert G. Wilson v_, Feb 03 2006
%E Added missing terms 134141, 142413, 194711 and a(24)-a(27) from _Donovan Johnson_, May 30 2010
%E a(28)-a(31) from _Chai Wah Wu_, Aug 27 2019