A324176 Integers k such that floor(sqrt(k)) + floor(sqrt(k/3)) divides k.

1, 2, 6, 15, 18, 24, 32, 36, 45, 55, 72, 78, 84, 98, 105, 112, 136, 144, 152, 180, 198, 220, 230, 275, 336, 390, 403, 462, 525, 540, 608, 663, 697, 756, 774, 792, 836, 855, 874, 940, 980, 1050, 1092, 1144, 1166, 1265, 1368, 1392, 1500, 1525, 1586, 1638, 1755, 1782, 1848, 1904

Offset: 1

Author

Jinyuan Wang, Mar 08 2019

Keywords

• nonn

Comments

This sequence is infinite for the same reason that A324175 is: if x-1 > y > 1 satisfies x^2 - 3*y^2 = -2 (x=A001834(j), y=A001835(j+1), j>0), then x < 3*y. Let k = 3*y^2 + m. By the pigeonhole principle there exists a number m belonging to [0, 2*x - 2] such that x + y | 3*y^2 + m, so such a k is a term.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001834, A001835, A324175.

Programs

Mathematica

Select[Range[2000],Divisible[#,Floor[Sqrt[#]]+Floor[Sqrt[#/3]]]&] (* Harvey P. Dale, Jun 19 2021 *)

PARI

is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/3))) == 0;