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A064523 Numbers n such that pi(n^2) is a square. 2

%I

%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 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

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Last modified October 16 03:24 EDT 2019. Contains 328038 sequences. (Running on oeis4.)