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

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn
• nice
• easy

Examples

			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
		

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

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

More terms from Michel ten Voorde

Definition corrected by Jonathan Sondow, Oct 28 2013