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

1, 3, 5, 10, 2640, 8304, 11699, 15330, 16810, 16910, 22463, 25906, 26652, 35950, 72429, 75470, 134141, 142413, 194711, 270353, 296073, 371964, 496254, 654609, 1640679, 1729409, 1854680, 4434965, 4973898, 5584120, 5783816

Offset: 1

Author

Jason Earls, Oct 07 2001

Keywords

• nonn
• more

Comments

a(28) > 2*10^6. [Donovan Johnson, May 30 2010]

Examples

			n = 14: a(14) = 35950, Pi(35950^2) = Pi(1292402500) = 64866916 = 8054^2
		

Crossrefs

Cf. A000720, A115835 (square root of pi(a(n))).

Programs

Mathematica

Do[ If[ IntegerQ[ Sqrt[ PrimePi[n^2]]], Print[n]], {n, 1, 400000} ]
lst = {}; Do[ If[ IntegerQ@ Sqrt@ PrimePi[n^2], AppendTo[lst, n]; Print@n], {n, 520000}]; lst (* Robert G. Wilson v, Feb 03 2006 *)

PARI

pi(x, c=0) = forprime(p=2,x,c++); c
for(n=1,10^6, if(issquare(pi(n^2)),print1(n,", ")))

Extensions

More terms from Robert G. Wilson v and Labos Elemer, Oct 08 2001

Further terms from Robert G. Wilson v, Oct 16 2001

a(20) from Robert G. Wilson v, Feb 03 2006

Added missing terms 134141, 142413, 194711 and a(24)-a(27) from Donovan Johnson, May 30 2010

a(28)-a(31) from Chai Wah Wu, Aug 27 2019