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A282094
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Larger member of a pair (x,y) which solves x^2 + y^2 = z^3 for nonnegative x, y and z.
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0
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0, 1, 2, 8, 10, 11, 16, 26, 27, 30, 39, 46, 52, 54, 64, 68, 80, 88, 100, 110, 117, 120, 125, 128, 130, 142, 145, 170, 198, 205, 208, 216, 222, 236, 240, 250, 270, 286, 297, 310, 312, 322, 343, 350, 366, 368, 371, 377, 406, 414, 415, 416, 432, 455, 481
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OFFSET
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1,3
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COMMENTS
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Values y such that x^2 + y^2 = z^3 has a solution 0 <= x <= y with integer x, y and z.
Differs from A282093 because solutions with x=0 are admitted; (x,y) = (0,t^3) solves the equation with z = t^2.
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LINKS
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FORMULA
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EXAMPLE
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0^2 + 0^2 = 0^3, so 0 is in. 0^2 + 1^2 = 1^3, so 1 is in. 2^2 + 2^2 = 2^3, so 2 is in. 0^2 + 8^2 = 4^3, so 8 is in. 5^2 + 10^2 = 5^3, so 10 is in.
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MAPLE
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isA282094 := proc(y)
local x, z3 ;
for x from 0 to y do
z3 := x^2+y^2 ;
if isA000578(z3) then
return true ;
end if;
end do:
return false ;
end proc:
for y from 0 to 800 do
if isA282094(y) then
printf("%d, ", y) ;
end if;
end do:
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MATHEMATICA
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isA282094[y_] := If[IntegerQ[y^(1/3)], True, Module[{x, z3}, For[x = 1, x <= y, x++, z3 = x^2 + y^2; If[IntegerQ[z3^(1/3)], Return[True]]]; Return[False]]];
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PROG
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(Python)
from sympy import factorint
def is_cube(n):
if n==0: return True
return all(i%3==0 for i in factorint(n).values())
def ok(n):
return any(is_cube(x**2 + n**2) for x in range(n + 1))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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