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

4, 15, 32, 40, 65, 85, 108, 120, 156, 175, 203, 256, 259, 272, 320, 369, 400, 405, 477, 500, 520, 580, 585, 671, 680, 715, 803, 820, 864, 888, 935, 960, 1080, 1105, 1111, 1157, 1248, 1261, 1372, 1400, 1417, 1464, 1484, 1624, 1625, 1695, 1755, 1820, 1875, 1885

Offset: 1

Author

César Eliud Lozada, Jul 27 2020

Keywords

• nonn
• easy

Comments

Numbers of the form (x+y)(x^2+y^2), where x and y are positive integers. - Chai Wah Wu, Aug 08 2020

No terms == 2 (mod 4). - Robert Israel, Sep 21 2020

Examples

			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, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024614.

Programs

Maple

N:= 10000: # for terms <= N
S:= {}:
for x from 1 while (x+1)*(x^2+1) < N do
   V:= select(`<=`,map(y -> (x+y)*(x^2+y^2), {seq(i,i=1..min(x,(N-x^3)/x^2))}),N);
   S:= S union V;
od:
sort(convert(S,list)); # Robert Israel, Sep 21 2020

Mathematica

max = 5000; T0 = {}; xm = Ceiling[Sqrt[max]]; While[T = T0;
T0 = Table[x^3 + x^2 y + x y^2 + y^3, {x, 1, xm}, {y, x, xm}] //
     Flatten // Union // Select[#, # <= max &] &; T != T0, xm = 2 xm];
T