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A050802
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Squares expressible as the sum of two positive cubes in at least one way.
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7
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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)
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OFFSET
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1,1
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REFERENCES
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"Game, Set and Math" by Ian Stewart, Chapter 8 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.
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LINKS
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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
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FORMULA
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a(n) = A050801(n)^2. - Jonathan Sondow, Oct 28 2013
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A038597, A050801, A050803, A106265, A217248.
Sequence in context: A171522 A236287 A329964 * A264519 A136313 A190322
Adjacent sequences: A050799 A050800 A050801 * A050803 A050804 A050805
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Patrick De Geest, Sep 15 1999
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EXTENSIONS
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More terms from Michel ten Voorde
Definition corrected by Jonathan Sondow, Oct 28 2013
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STATUS
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approved
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