A324177 Integers k such that floor(sqrt(k)) + floor(sqrt(k/4)) divides k.

1, 2, 3, 6, 12, 18, 24, 28, 35, 36, 45, 50, 60, 72, 91, 105, 120, 128, 144, 162, 171, 190, 210, 242, 264, 288, 300, 324, 351, 364, 392, 420, 465, 495, 528, 544, 576, 612, 629, 666, 702, 760, 798, 840, 860, 900, 945, 966, 1012, 1056, 1127, 1173, 1224, 1248, 1296

Offset: 1

Author

Jinyuan Wang, Mar 09 2019

Keywords

• nonn

Comments

k = 36*j^2 is a term for j > 0.

Other infinite families of terms are 36*j^2-29*j+5, 36*j^2-21*j+3, 36*j^2-12*j, 36*j^2-8*j,36*j^2+9*j,36*j^2+13*j+1,36*j^2+22*j+2, and 36*j^2+30*j+6. These cover all terms <= 4676406 except 35. - Robert Israel, Jan 24 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..3200

Crossrefs

Cf. A324174, A324175, A324176, A324178.

Programs

Maple

filter:= n -> n mod (floor(sqrt(n))+floor(sqrt(n/4))) = 0:
select(filter, [$1..10000]); # Robert Israel, Jan 24 2020

Mathematica

Select[Range[1296], Mod[#, Floor@ Sqrt@ # + Floor@ Sqrt[#/4]] == 0 &] (* Giovanni Resta, Apr 05 2019 *)

PARI

is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/4))) == 0;