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A307585 Positive sums of two distinct cubes (of arbitrary sign).

%I A307585 #16 Oct 19 2020 12:35:54
%S A307585 1,7,8,9,19,26,27,28,35,37,56,61,63,64,65,72,91,98,117,124,125,126,
%T A307585 127,133,152,169,189,208,215,216,217,218,224,243,271,279,280,296,316,
%U A307585 331,335,341,342,343,344,351,370,386,387,397,407,448,468,469,485,488,504,511,512,513,520,539,547,559
%N A307585 Positive sums of two distinct cubes (of arbitrary sign).
%C A307585 All terms == 0, 1, 2, 7 or 8 (mod 9).
%H A307585 Robert Israel, <a href="/A307585/b307585.txt">Table of n, a(n) for n = 1..10000</a>
%H A307585 <a href="/index/Su#ssq">Index to sequences related to sums of cubes</a>
%e A307585 a(3) = 8 = 0^3 + 2^3.
%e A307585 a(4) = 9 = 1^3 + 2^3.
%e A307585 a(5) = 19 = (-2)^3 + 3^3.
%p A307585 filter:= proc(n) local d, dp, r;
%p A307585    for d in numtheory:-divisors(n) do
%p A307585      dp:= n/d;
%p A307585      r:= 12*dp - 3*d^2;
%p A307585      if r > 0 and issqr(r) and (sqrt(r)/6 + d/2)::integer then return true fi
%p A307585    od;
%p A307585    false
%p A307585 end proc:
%p A307585 select(filter, [$0..1000]);
%t A307585 filterQ[n_] := Module[{d, dp, r}, Catch[Do[dp = n/d; r = 12 dp - 3 d^2; If[r > 0 && IntegerQ[Sqrt[r]] && IntegerQ[Sqrt[r]/6 + d/2], Throw[True]], {d, Divisors[n]}]; False]];
%t A307585 Select[Range[1000], filterQ] (* _Jean-François Alcover_, Oct 17 2020, after Maple *)
%Y A307585 Contained in A045980.  Contains A024670.
%Y A307585 Primes in this sequence: A002407.
%Y A307585 Cf. A060464.
%K A307585 nonn
%O A307585 1,2
%A A307585 _Robert Israel_, Apr 15 2019