A050802 Squares expressible as the sum of two positive cubes in at least one way.

9, 16, 576, 1024, 6561, 9604, 11664, 28224, 36864, 51984, 65536, 97344, 140625, 250000, 275625, 345744, 419904, 450241, 614656, 717409, 746496, 1028196, 1058841, 1399489, 1500625, 1590121, 1750329, 1806336, 1882384, 2359296

Offset

1,1

References

"Game, Set and Math" by Ian Stewart, Chapter 8 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.

Links

Tony D. Noe and Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for sequences related to sums of squares

Formula

a(n) = A050801(n)^2. - Jonathan Sondow, Oct 28 2013

Example

E.g., 717409 = 847^2 = 33^3 + 88^3.
169 = 13^2 = (-7)^3 + 8^3 is not a member, because 169 is not the sum of two positive cubes. - Jonathan Sondow, Oct 28 2013

Mathematica

ok[n_] := Length[Select[PowersRepresentations[n, 2, 3], #[[1]] != 0 & ]] >= 1; Select[Range[1600]^2, ok]
(* Jean-François Alcover, Apr 22 2011 *)
Union[Select[Total/@Tuples[Range[250]^3, 2], IntegerQ[Sqrt[#]]&]] (* Harvey P. Dale, Mar 04 2012 *)

Prog

(PARI) { nstart=1; a2start=9; n=nstart; a=sqrtint(a2start)-1; until (0, a=a+1; a2=a*a; b1=((a2/2)^(1/3))\1; for (b=b1, a, b3=b*b*b; c1=1; if (a2 > b3, c1=((a2-b3)^(1/3))\1; ); for (c=c1, b, d=b3 + c*c*c; if (d > a2 && c == 1, break(2)); if (d > a2, break); if (a2 == d, print(n, " ", a2); write("b050802.txt", n, " ", a2); n=n+1; break(2); ); ) ) ) } \\ Harry J. Smith, Jan 15 2009
(PARI) is(n)=for(k=sqrtnint((n+1)\2, 3), sqrtnint(n-1, 3), if(ispower(n-k^3, 3), return(issquare(n)))); 0 \\ Charles R Greathouse IV, Oct 28 2013

Crossrefs

Cf. A038597, A050801, A050803, A106265, A217248.

Sequence in context: A171522 A236287 A329964 * A264519 A136313 A190322

Adjacent sequences: A050799 A050800 A050801 * A050803 A050804 A050805

Keyword

nonn,nice,easy

Author

Patrick De Geest, Sep 15 1999

Extensions

More terms from Michel ten Voorde

Definition corrected by Jonathan Sondow, Oct 28 2013

Status

approved