A324178 Integers k such that floor(sqrt(k)) + floor(sqrt(k/5)) divides k.

1, 2, 3, 4, 6, 12, 24, 28, 35, 40, 45, 50, 60, 66, 77, 91, 112, 128, 153, 190, 200, 220, 231, 276, 312, 338, 378, 406, 435, 450, 480, 496, 512, 561, 578, 648, 703, 722, 741, 780, 800, 840, 882, 903, 946, 968, 990, 1058, 1152, 1176, 1250, 1300, 1352, 1378

Offset: 1

Author

Jinyuan Wang, Mar 09 2019

Keywords

• nonn

Comments

This sequence is infinite for the same reason that A324175 is: if x > y satisfies x^2 - 5*y^2 = -1 (x=A075796(j), y=A007805(j-1), j>0), then x < 5*y. Let k = 5*y^2 + m. By the pigeonhole principle there exists a number m belonging to [0, 2*x - 1] such that x + y | 5*y^2 + m, so such a k is a term.

Crossrefs

Cf. A007805, A075796, A324174, A324175, A324176, A324177.

Programs

Mathematica

Select[Range[1378], Mod[#, Floor@ Sqrt@ # + Floor@ Sqrt[#/5]] == 0 &] (* Giovanni Resta, Apr 05 2019 *)

PARI

is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/5))) == 0;