A230314 Numbers that are simultaneously the sum of two nonnegative squares and the sum of two nonnegative cubes.

0, 1, 2, 8, 9, 16, 64, 65, 72, 125, 128, 250, 370, 468, 512, 520, 576, 637, 729, 730, 793, 1000, 1024, 1125, 1241, 1332, 1458, 1853, 2000, 2197, 2205, 2745, 2960, 3528, 3744, 3925, 4096, 4097, 4160, 4394, 4608, 4706, 4825, 4913, 4941, 5096, 5256, 5832, 5840

Offset

1,3

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

72 is in the sequence because 6^2 + 6^2 = 4^3 + 2^3 = 72.
73 is not in the sequence, because, although it can be expressed as the sum of two squares (8^2 + 3^2), it can't be expressed as the sum of two cubes.

Maple

s_sq0:=proc(n) local i, f; f:=false:
for i from 0 while 2*i^2<=n do
if type(sqrt(n-i^2), nonnegint) then f:=true:break fi od;
f end;
s_cb0:=proc(n) local i, f; f:=false:
for i from 0 while 2*i^3<=n do
if type(surd(n-i^3, 3), nonnegint) then f:=true:break fi od;
f end;
for n from 0 do if s_sq0(n) and s_cb0(n)then print(n) fi od:

Mathematica

n2 = 80; n3 = Ceiling[n2^(2/3)]; t2 = Flatten[Table[a^2 + b^2, {a, 0, n2}, {b, a, n2}]]; t3 = Flatten[Table[a^3 + b^3, {a, 0, n3}, {b, a, n3}]]; Intersection[Union[Select[t2, # <= n2^2 &]], Union[Select[t3, # <= n3^3 &]]] (* T. D. Noe, Oct 18 2013 *)

Crossrefs

Cf. A001481, A004999, A229815.

Sequence in context: A046679 A004999 A105125 * A220263 A033492 A126160

Adjacent sequences: A230311 A230312 A230313 * A230315 A230316 A230317

Keyword

nonn

Author

Vladimir Letsko, Oct 15 2013

Status

approved