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A050802 Squares expressible as the sum of two positive cubes in at least one way. 7
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A053911 A171522 A236287 * 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 (seqfan(AT)tenvoorde.org)

Definition corrected by Jonathan Sondow, Oct 28 2013

STATUS

approved

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Last modified May 29 22:45 EDT 2017. Contains 287257 sequences.