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A229815
Numbers that are simultaneously the sum of two positive squares and the sum of two positive cubes.
2
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
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
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Sep 30 2013
STATUS
approved