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A293645
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Positive numbers that are the sum of two (possibly negative) coprime cubes.
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4
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1, 2, 7, 9, 19, 26, 28, 35, 37, 61, 63, 65, 91, 98, 117, 124, 126, 127, 133, 152, 169, 189, 215, 217, 218, 271, 279, 316, 331, 335, 341, 342, 344, 351, 370, 386, 387, 397, 407, 468, 469, 485, 511, 513, 539, 547, 559, 602, 604, 631, 637, 657, 665, 721, 728, 730
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OFFSET
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1,2
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COMMENTS
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Also sum or difference of two coprime cubes. - David A. Corneth, Oct 20 2017
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LINKS
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David A. Corneth, Table of n, a(n) for n = 1..10000, (first 101 terms from Rosalie Fay).
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EXAMPLE
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19 = 3^3 + (-2)^3, where 3 and -2 are coprime, so 19 is in the sequence.
152 = 5^3 + 3^3, where 5 and 3 are coprime, so 152 is in the sequence.
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MAPLE
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filter:= proc(n) local s, x, y;
for s in numtheory:-divisors(n) do
x:= s/2 + sqrt(12*n/s-3*s^2)/6;
if not x::integer then next fi;
y:= s - x;
if igcd(x, y) = 1 then return true fi;
od;
false
end proc:
select(filter, [seq(seq(9*i+j, j=[1, 2, 7, 8, 9]), i=0..1000)]); # Robert Israel, Oct 22 2017
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PROG
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(PARI) upto(lim) = {my(res = List([2]), c, i, j); for(i=1, sqrtnint(lim, 3), for(j=0, sqrtnint(lim - i^3, 3), if(gcd(i, j) == 1, listput(res, c)))); for(i=1, sqrtint(lim\3)+1, for(j = 1, i, if(gcd(i, j) == 1, c = i^3 - (i-j)^3; if(c<=lim, listput(res, c), next(2))))); listsort(res, 1); res} \\ David A. Corneth, Oct 20 2017
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CROSSREFS
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Cf. A003325 (positive cubes); A020895 (cubefree); A293646 (only coprime); A293647, A293650.
Sequence in context: A079326 A055673 A177737 * A293646 A020895 A174247
Adjacent sequences: A293642 A293643 A293644 * A293646 A293647 A293648
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KEYWORD
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nonn,easy
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AUTHOR
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Rosalie Fay, Oct 16 2017
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STATUS
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approved
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