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%I #8 Apr 05 2019 10:03:44
%S 1,2,3,4,6,12,24,28,35,40,45,50,60,66,77,91,112,128,153,190,200,220,
%T 231,276,312,338,378,406,435,450,480,496,512,561,578,648,703,722,741,
%U 780,800,840,882,903,946,968,990,1058,1152,1176,1250,1300,1352,1378
%N Integers k such that floor(sqrt(k)) + floor(sqrt(k/5)) divides k.
%C 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.
%t Select[Range[1378], Mod[#, Floor@ Sqrt@ # + Floor@ Sqrt[#/5]] == 0 &] (* _Giovanni Resta_, Apr 05 2019 *)
%o (PARI) is(n) = n%(floor(sqrt(n)) + floor(sqrt(n/5))) == 0;
%Y Cf. A007805, A075796, A324174, A324175, A324176, A324177.
%K nonn
%O 1,2
%A _Jinyuan Wang_, Mar 09 2019
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