login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Integers k such that floor(sqrt(k)) + floor(sqrt(k/4)) divides k.
3

%I #12 Jan 24 2020 15:37:18

%S 1,2,3,6,12,18,24,28,35,36,45,50,60,72,91,105,120,128,144,162,171,190,

%T 210,242,264,288,300,324,351,364,392,420,465,495,528,544,576,612,629,

%U 666,702,760,798,840,860,900,945,966,1012,1056,1127,1173,1224,1248,1296

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

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

%C 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

%H Robert Israel, <a href="/A324177/b324177.txt">Table of n, a(n) for n = 1..3200</a>

%p filter:= n -> n mod (floor(sqrt(n))+floor(sqrt(n/4))) = 0:

%p select(filter, [$1..10000]); # _Robert Israel_, Jan 24 2020

%t Select[Range[1296], Mod[#, Floor@ Sqrt@ # + Floor@ Sqrt[#/4]] == 0 &] (* _Giovanni Resta_, Apr 05 2019 *)

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

%Y Cf. A324174, A324175, A324176, A324178.

%K nonn

%O 1,2

%A _Jinyuan Wang_, Mar 09 2019