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A336607 Numbers of the form x^3 + x^2*y + x*y^2 + y^3, where x and y are positive integers.

%I A336607 #17 Sep 22 2020 02:44:24
%S A336607 4,15,32,40,65,85,108,120,156,175,203,256,259,272,320,369,400,405,477,
%T A336607 500,520,580,585,671,680,715,803,820,864,888,935,960,1080,1105,1111,
%U A336607 1157,1248,1261,1372,1400,1417,1464,1484,1624,1625,1695,1755,1820,1875,1885
%N A336607 Numbers of the form x^3 + x^2*y + x*y^2 + y^3, where x and y are positive integers.
%C A336607 Numbers of the form (x+y)(x^2+y^2), where x and y are positive integers. - _Chai Wah Wu_, Aug 08 2020
%C A336607 No terms == 2 (mod 4). - _Robert Israel_, Sep 21 2020
%H A336607 Robert Israel, <a href="/A336607/b336607.txt">Table of n, a(n) for n = 1..10000</a>
%e A336607 4=1^3+1^2*1+1*1^2+1^3, 15=1^3+1^2*2+1*2^2+2^3, 32=2^3+2^2*2+2*2^2+2^3, ...
%p A336607 N:= 10000: # for terms <= N
%p A336607 S:= {}:
%p A336607 for x from 1 while (x+1)*(x^2+1) < N do
%p A336607    V:= select(`<=`,map(y -> (x+y)*(x^2+y^2), {seq(i,i=1..min(x,(N-x^3)/x^2))}),N);
%p A336607    S:= S union V;
%p A336607 od:
%p A336607 sort(convert(S,list)); # _Robert Israel_, Sep 21 2020
%t A336607 max = 5000; T0 = {}; xm = Ceiling[Sqrt[max]]; While[T = T0;
%t A336607 T0 = Table[x^3 + x^2 y + x y^2 + y^3, {x, 1, xm}, {y, x, xm}] //
%t A336607      Flatten // Union // Select[#, # <= max &] &; T != T0, xm = 2 xm];
%t A336607 T
%Y A336607 Cf. A024614.
%K A336607 nonn,easy
%O A336607 1,1
%A A336607 _César Eliud Lozada_, Jul 27 2020