cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A064523 #28 May 05 2025 03:52:59
%S A064523 1,3,5,10,2640,8304,11699,15330,16810,16910,22463,25906,26652,35950,
%T A064523 72429,75470,134141,142413,194711,270353,296073,371964,496254,654609,
%U A064523 1640679,1729409,1854680,4434965,4973898,5584120,5783816
%N A064523 Numbers m such that pi(m^2) is a square.
%C A064523 a(28) > 2*10^6. [_Donovan Johnson_, May 30 2010]
%e A064523 n = 14: a(14) = 35950, Pi(35950^2) = Pi(1292402500) = 64866916 = 8054^2
%t A064523 Do[ If[ IntegerQ[ Sqrt[ PrimePi[n^2]]], Print[n]], {n, 1, 400000} ]
%t A064523 lst = {}; Do[ If[ IntegerQ@ Sqrt@ PrimePi[n^2], AppendTo[lst, n]; Print@n], {n, 520000}]; lst (* _Robert G. Wilson v_, Feb 03 2006 *)
%o A064523 (PARI) pi(x, c=0) = forprime(p=2,x,c++); c
%o A064523 for(n=1,10^6, if(issquare(pi(n^2)),print1(n,", ")))
%Y A064523 Cf. A000720, A115835 (square root of pi(a(n))).
%K A064523 nonn,more
%O A064523 1,2
%A A064523 _Jason Earls_, Oct 07 2001
%E A064523 More terms from _Robert G. Wilson v_ and _Labos Elemer_, Oct 08 2001
%E A064523 Further terms from _Robert G. Wilson v_, Oct 16 2001
%E A064523 a(20) from _Robert G. Wilson v_, Feb 03 2006
%E A064523 Added missing terms 134141, 142413, 194711 and a(24)-a(27) from _Donovan Johnson_, May 30 2010
%E A064523 a(28)-a(31) from _Chai Wah Wu_, Aug 27 2019