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

1,2

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001834, A001835, A324175.

Sequence in context: A134891 A020947 A011777 * A294942 A227307 A129631

Adjacent sequences: A324173 A324174 A324175 * A324177 A324178 A324179

Keyword

nonn

Author

Jinyuan Wang, Mar 08 2019

Status

approved