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

1,1

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

Links

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

Example

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, ...

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

Crossrefs

Cf. A024614.

Sequence in context: A322740 A366659 A121914 * A321490 A270710 A322571

Adjacent sequences: A336604 A336605 A336606 * A336608 A336609 A336610

Keyword

nonn,easy

Author

César Eliud Lozada, Jul 27 2020

Status

approved