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

1,1

Links

Table of n, a(n) for n=1..52.

Example

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

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}]]

Prog

(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

Crossrefs

Cf. A006446.

Sequence in context: A290172 A031407 A267826 * A361627 A002505 A182438

Adjacent sequences: A339470 A339471 A339472 * A339474 A339475 A339476

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 24 2021

Status

approved