cp's OEIS Frontend

A259227 Hydropronic numbers: numbers n that can be written as a product of 2 integers whose sum is equal to ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)).

%I A259227 #11 Oct 16 2016 18:48:27
%S A259227 1,2,3,4,6,8,9,10,12,15,16,18,20,21,24,25,28,30,32,35,36,40,42,45,48,
%T A259227 49,50,54,56,60,63,64,66,70,72,77,80,81,84,88,90,91,96,99,100,104,108,
%U A259227 110,112,117,120,121,126,130,132,135,140,143,144,150,154,156,160
%N A259227 Hydropronic numbers: numbers n that can be written as a product of 2 integers whose sum is equal to ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)).
%C A259227 It appears that ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)) is A027434(n).
%H A259227 Ivan Neretin, <a href="/A259227/b259227.txt">Table of n, a(n) for n = 1..10000</a>
%H A259227 Casey Douglas, <a href="https://mathematicalypse.wordpress.com/2012/06/24/the-next-square-or-pronic/">The Next Square or Pronic</a>, June 2012.
%H A259227 Casey Douglas, <a href="https://mathematicalypse.wordpress.com/2012/06/20/hydropronic-sequence/">Hydropronic Sequence?</a>, June 2012.
%H A259227 Casey Douglas, <a href="https://mathematicalypse.wordpress.com/2012/07/11/another-quickie/">Another Quickie</a>, July 2012.
%t A259227 Select[Range@160, IntegerQ@Sqrt[((r = Ceiling@Sqrt@#) + Ceiling[#/r])^2 - 4 #] &] (* _Ivan Neretin_, Oct 16 2016 *)
%o A259227 (PARI) isok(n) = {d = divisors(n); for (k=1, #d, if ((d[k] + n/d[k]) == ceil(n/ceil(sqrt(n)))+ceil(sqrt(n)), return (1)););}
%K A259227 nonn
%O A259227 1,2
%A A259227 _Michel Marcus_, Jun 21 2015