A064523 - OEIS

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A064523

Numbers n such that pi(n^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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A354517 A354389 A297422 * A365443 A268034 A286567

Adjacent sequences: A064520 A064521 A064522 * A064524 A064525 A064526

KEYWORD

nonn

AUTHOR

Jason Earls, Oct 07 2001

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

STATUS

approved