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A217248 Numbers whose square is the sum of two nonnegative cubes. 4
0, 1, 3, 4, 8, 24, 27, 32, 64, 81, 98, 108, 125, 168, 192, 216, 228, 256, 312, 343, 375, 500, 512, 525, 588, 648, 671, 729, 784, 847, 864, 1000, 1014, 1029, 1183, 1225, 1261, 1323, 1331, 1344, 1372, 1536, 1728, 1824, 2048, 2187, 2197, 2496, 2646, 2744, 2888 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers N such that N^2 = x^3 + y^3 where x and y are nonnegative integers. First case with 2 solutions is 77976^2 = 228^3 + 1824^3 = 1026^3 + 1710^3, see A051302. - Zak Seidov, Mar 21 2013

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..5000

EXAMPLE

312 is in the sequence because 312^2 = 2^3 + 46^3.

MATHEMATICA

m = 2888; Sort[Reap[Do[If[IntegerQ[c = Sqrt[a^3 + b^3]], Sow[c]], {a, 0, m^(2/3)}, {b, a, (m^2 - a^3)^(1/3)}]][[2, 1]]] (* Zak Seidov, Mar 21 2013 *)

PROG

(R)

  y=c(); maxsol=3000 #All solutions <this value

  for(i in 0:(maxsol^(2/3))) for(j in i:((maxsol^2-i^3)^(1/3)))

      if(i<=j & 2*i^3<maxsol^2) if((sqrt(i^3+j^3)->x)==as.integer(x))y=c(y, x)

sort(y)

(PARI) is(n)=n*=n; for(k=ceil((n/2-.5)^(1/3)), (n+.5)^(1/3), if(ispower(n-k^3, 3), return(1))); 0 \\ Charles R Greathouse IV, Mar 20 2013

CROSSREFS

This sequence with only positive (nonzero) cubes: A050801, and that sequence squared: A050802

A natural extension of the hypotenuse numbers A009003.

Sequence in context: A101932 A204521 A073313 * A168382 A155701 A119529

Adjacent sequences:  A217245 A217246 A217247 * A217249 A217250 A217251

KEYWORD

nonn

AUTHOR

Christian N. K. Anderson & Kevin L. Schwartz, Mar 20 2013

EXTENSIONS

Offset and a(35) corrected and a(36)-a(51) from Giovanni Resta, Mar 20 2013

STATUS

approved

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Last modified February 27 05:58 EST 2020. Contains 332299 sequences. (Running on oeis4.)