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A282094 Larger member of a pair (x,y) which solves x^2 + y^2 = z^3 for nonnegative x, y and z. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Equals A282093 union A000578.

EXAMPLE

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.

MAPLE

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:

PROG

(Python)

from sympy import factorint

def is_cube(n):

    if n==0: return 1

    for i in factorint(n).values():

        if i%3!=0: return 0

    return 1

def ok(n):

for x in range(n + 1):

        z=x**2 + n**2

        if is_cube(z): return 1

    return 0

print [n for n in range(501) if ok(n)] # Indranil Ghosh, Jun 30 2017

(PARI) is(n)=my(n2=n^2); for(x=0, n, if(ispower(n2+x^2, 3), return(1))); 0 \\ Charles R Greathouse IV, Jun 30 2017

CROSSREFS

Cf. A282093.

Sequence in context: A139370 A101532 A032708 * A084124 A081693 A022298

Adjacent sequences:  A282091 A282092 A282093 * A282095 A282096 A282097

KEYWORD

nonn

AUTHOR

R. J. Mathar, Feb 06 2017

STATUS

approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)