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

1,2

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.

Links

Table of n, a(n) for n=1..54.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A102462 A277408 A018369 * A214570 A306348 A363670

Adjacent sequences: A324175 A324176 A324177 * A324179 A324180 A324181

Keyword

nonn

Author

Jinyuan Wang, Mar 09 2019

Status

approved