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 A023042 Numbers whose cube is the sum of three distinct nonnegative cubes. 11
 6, 9, 12, 18, 19, 20, 24, 25, 27, 28, 29, 30, 36, 38, 40, 41, 42, 44, 45, 46, 48, 50, 53, 54, 56, 57, 58, 60, 63, 66, 67, 69, 70, 71, 72, 75, 76, 78, 80, 81, 82, 84, 85, 87, 88, 89, 90, 92, 93, 95, 96, 97, 99, 100, 102, 103, 105, 106, 108, 110, 111, 112, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers w such that w^3 = x^3+y^3+z^3, x>y>z>=0, is soluble. A226903(n) + 1 is an infinite subsequence parametrized by Shiraishi in 1826. - Jonathan Sondow, Jun 22 2013 Because of Fermat's Last Theorem, sequence lists numbers w such that w^3 = x^3+y^3+z^3, x>y>z>0, is soluble. In other words, z cannot be 0 because x and y are positive integers by definition of this sequence. - Altug Alkan, May 08 2016 This sequence is the same as numbers w such that w^3 = x^3+y^3+z^3, x>=y>=z>0, is soluble as Legendre showed that a^3+b^3=2*c^3 only has the trivial solutions a = b or a = -b (see Dickson’s History of the Theory of Numbers, vol. II, p. 573). - Chai Wah Wu, May 13 2017 REFERENCES Ya. I. Perelman, Algebra can be fun, pp. 142-143. LINKS Nathaniel Johnston and Chai Wah Wu, Table of n, a(n) for n = 1..10000 (1..1500 from Nathaniel Johnston) A. Russell and C. E. Gwyther, The Partition of Cubes, The Mathematical Gazette, 21 (1937), pp. 33-35. EXAMPLE 20 belongs to the sequence as 20^3 = 7^3 + 14^3 + 17^3. MAPLE for w from 1 to 113 do for z from 0 to w-1 do bk:=0: for y from z+1 to w-1 do for x from y+((w+z) mod 2) to w-1 by 2 do if(x^3+y^3+z^3=w^3)then printf("%d, ", w); bk:=1: break: fi: od: if(bk=1)then break: fi: od: if(bk=1)then break: fi: od: od: # Nathaniel Johnston, Jun 22 2013 MATHEMATICA lst={}; Do[Do[Do[Do[y=a^3+b^3+c^3; x=z^3; If[ylim, sqrtnint(a3-lim-1, 3)+1, 1), a-1, t=a3-b^3; if(has(t), listput(v, a)))); Set(v) \\ Charles R Greathouse IV, Jan 25 2018 CROSSREFS Cf. A001235, A003072, A114923, A225908, A226903. Sequence in context: A020938 A136360 A023483 * A128245 A117714 A245685 Adjacent sequences:  A023039 A023040 A023041 * A023043 A023044 A023045 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 24 09:55 EDT 2019. Contains 324323 sequences. (Running on oeis4.)