A135782 - OEIS

%I #14 Jul 03 2024 13:19:38

%S 2,9,10,11,16,26,36,38,44,46,47,54,72,74,80,88,107,115,117,128,135,

%T 142,146,182,187,191,198,208,234,236,242,243,250,270,286,288,297,299,

%U 304,341,352,362,368,376,413,414,415,431,432,470,478,504,506,524,530,549

%N Positive numbers of the form 3*x*y^2 - x^3 (where x,y are positive integers).

%H Robert Israel, <a href="/A135782/b135782.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 10^4: # for terms <= N

%p S:= {}:

%p for x from 1 to floor(N/2) do

%p   S:= S union {seq(3*x*y^2 - x^3, y = ceil(x/sqrt(3)) .. floor(sqrt((x^2+N/x)/3)))}

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Aug 14 2023

%t a = {}; Do[Do[w = 3x y^2 - x^3; If[(w > 0) && w < 3000, AppendTo[a, w]], {x, 1, 1000}], {y, 1, 1000}]; Union[a]

%t With[{nn=300},Select[Flatten[Table[3*x*y^2-x^3,{x,nn},{y,nn}]],0<#<600&]//Union] (* _Harvey P. Dale_, Jul 03 2024 *)

%Y Cf. A135781, A364974.

%K nonn

%O 1,1

%A _Artur Jasinski_, Nov 29 2007