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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A324174, A324175, A324176, A324178.

Sequence in context: A032727 A323392 A174801 * A280681 A328899 A093687

Adjacent sequences: A324174 A324175 A324176 * A324178 A324179 A324180

Keyword

nonn

Author

Jinyuan Wang, Mar 09 2019

Status

approved