A339473 Numbers k such that floor(sqrt(k)) divides k^2, but does not divide k.

18, 22, 68, 76, 84, 87, 93, 96, 150, 162, 260, 264, 268, 276, 280, 284, 330, 336, 348, 354, 410, 430, 588, 612, 630, 635, 640, 645, 655, 660, 665, 670, 738, 747, 765, 774, 798, 826, 1032, 1040, 1048, 1064, 1072, 1080, 1302, 1308, 1314, 1320, 1326, 1338, 1344, 1350

Offset: 1

Author

Wesley Ivan Hurt, Apr 24 2021

Keywords

• nonn

Examples

			18 is in the sequence since floor(sqrt(18)) = 4, which does not divide 18, but it does divide 18^2 = 324.
		

Crossrefs

Cf. A006446.

Programs

Mathematica

Flatten[Table[If[(1 - Ceiling[n^2/Floor[Sqrt[n]]] + Floor[n^2/Floor[Sqrt[n]]]) (Ceiling[n/Floor[Sqrt[n]]] - Floor[n/Floor[Sqrt[n]]]) == 1, n, {}], {n, 2000}]]

PARI

isok(k) = (k % sqrtint(k)) && !(k^2 % sqrtint(k)); \\ Michel Marcus, Apr 24 2021

Python

from math import isqrt
def ok(k): r = isqrt(k); return k % r != 0 and k**2 % r == 0
print(list(filter(ok, range(1, 1351)))) # Michael S. Branicky, Apr 24 2021