A229815 Numbers that are simultaneously the sum of two positive squares and the sum of two positive cubes.

2, 65, 72, 128, 250, 370, 468, 520, 637, 730, 793, 1125, 1241, 1332, 1458, 1853, 2000, 2205, 2745, 2960, 3528, 3744, 3925, 4097, 4160, 4394, 4608, 4706, 4825, 4941, 5096, 5256, 5840, 5913, 6344, 6641, 6984, 7202, 8125, 8192, 9000, 9325, 9386, 9477, 9773, 9826

Offset

1,1

Links

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

Example

520 is in the sequence because 520 = 22^2 + 6^2 = 8^3 + 2^3.

Maple

s_sq:=proc(n) local i, f; f:=false:
for i while 2*i^2<=n do
if type(sqrt(n-i^2), posint) then f:=true:break fi od;
f end;
s_cb:=proc(n) local i, f; f:=false:
for i while 2*i^3<=n do
if type(surd(n-i^3, 3), posint) then f:=true:break fi od;
f end;
for n to do if s_sq(n) and s_cb(n)then prunt(n) fi od:

Mathematica

n2 = 100; n3 = Ceiling[n2^(2/3)]; t2 = Flatten[Table[a^2 + b^2, {a, n2}, {b, a, n2}]]; t3 = Flatten[Table[a^3 + b^3, {a, n3}, {b, a, n3}]]; Intersection[Union[Select[t2, # <= n2^2 &]], Union[Select[t3, # <= n3^3 &]]] (* T. D. Noe, Oct 18 2013 *)

Crossrefs

Cf. A000404, A003325, A230314.

Sequence in context: A337651 A287649 A229352 * A273498 A003358 A303376

Adjacent sequences: A229812 A229813 A229814 * A229816 A229817 A229818

Keyword

nonn

Author

Vladimir Letsko, Sep 30 2013

Status

approved