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 A307585 Positive sums of two distinct cubes (of arbitrary sign). 1
 1, 7, 8, 9, 19, 26, 27, 28, 35, 37, 56, 61, 63, 64, 65, 72, 91, 98, 117, 124, 125, 126, 127, 133, 152, 169, 189, 208, 215, 216, 217, 218, 224, 243, 271, 279, 280, 296, 316, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All terms == 0, 1, 2, 7 or 8 (mod 9). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Index to sequences related to sums of cubes EXAMPLE a(3) = 8 = 0^3 + 2^3. a(4) = 9 = 1^3 + 2^3. a(5) = 19 = (-2)^3 + 3^3. MAPLE filter:= proc(n) local d, dp, r; for d in numtheory:-divisors(n) do dp:= n/d; r:= 12*dp - 3*d^2; if r > 0 and issqr(r) and (sqrt(r)/6 + d/2)::integer then return true fi od; false end proc: select(filter, [\$0..1000]); MATHEMATICA 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]]; Select[Range[1000], filterQ] (* Jean-François Alcover, Oct 17 2020, after Maple *) CROSSREFS Contained in A045980. Contains A024670. Primes in this sequence: A002407. Cf. A060464. Sequence in context: A165480 A285468 A060258 * A347809 A048029 A048009 Adjacent sequences: A307582 A307583 A307584 * A307586 A307587 A307588 KEYWORD nonn AUTHOR Robert Israel, Apr 15 2019 STATUS approved

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Last modified September 15 01:56 EDT 2024. Contains 375929 sequences. (Running on oeis4.)