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

%I A324177 #12 Jan 24 2020 15:37:18
%S A324177 1,2,3,6,12,18,24,28,35,36,45,50,60,72,91,105,120,128,144,162,171,190,
%T A324177 210,242,264,288,300,324,351,364,392,420,465,495,528,544,576,612,629,
%U A324177 666,702,760,798,840,860,900,945,966,1012,1056,1127,1173,1224,1248,1296
%N A324177 Integers k such that floor(sqrt(k)) + floor(sqrt(k/4)) divides k.
%C A324177 k = 36*j^2 is a term for j > 0.
%C A324177 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 A324177 Robert Israel, <a href="/A324177/b324177.txt">Table of n, a(n) for n = 1..3200</a>
%p A324177 filter:= n -> n mod (floor(sqrt(n))+floor(sqrt(n/4))) = 0:
%p A324177 select(filter, [$1..10000]); # _Robert Israel_, Jan 24 2020
%t A324177 Select[Range[1296], Mod[#, Floor@ Sqrt@ # + Floor@ Sqrt[#/4]] == 0 &] (* _Giovanni Resta_, Apr 05 2019 *)
%o A324177 (PARI) is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/4))) == 0;
%Y A324177 Cf. A324174, A324175, A324176, A324178.
%K A324177 nonn
%O A324177 1,2
%A A324177 _Jinyuan Wang_, Mar 09 2019