A069186 Numbers n such that core(n)=floor(sqrt(n)), where core(x)=A007913(x) is the squarefree part of x and floor(sqrt(x))=A000196(x).

1, 8, 12, 63, 224, 240, 575, 1224, 1260, 2303, 3968, 6399, 14399, 20448, 20592, 28223, 38024, 38220, 50175, 65024, 65280, 82943, 104328, 104652, 129599, 159200, 159600, 193599, 233288, 233772, 278783, 330624, 389375, 455624

Offset: 1

Author

Benoit Cloitre, Apr 14 2002

Keywords

• easy
• nonn

Comments

Apart from 1, numbers of the form x*y^2 for y >= 2, where x is squarefree and is either y^2-2 or y^2-1. - Robert Israel, Apr 11 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000196, A007913.

Programs

Maple

select(numtheory:-issqrfree, [1, seq(seq(b^2+j,j=-2..-1),b=2..100)]); # Robert Israel, Apr 11 2019

PARI

isok(n) = core(n) == sqrtint(n); \\ Michel Marcus, Apr 12 2019

Extensions

Name edited by Robert Israel, Apr 12 2019