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A324176
Integers k such that floor(sqrt(k)) + floor(sqrt(k/3)) divides k.
4
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
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
KEYWORD
nonn
AUTHOR
Jinyuan Wang, Mar 08 2019
STATUS
approved