

A023042


Numbers w such that w^3 = x^3+y^3+z^3, x>y>z>=0, is soluble.


7



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
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OFFSET

1,1


COMMENTS

Numbers whose cube is the sum of three nonnegative cubes.
A226903(n) + 1 is an infinite subsequence parametrized by Shiraishi in 1826.  Jonathan Sondow, Jun 22 2013


REFERENCES

Ya. I. Perelman, Algebra can be fun, pp. 142143.


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..1500


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 w1 do bk:=0: for y from z+1 to w1 do for x from y+((w+z) mod 2) to w1 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[y<x, Break[], If[y==x, AppendTo[lst, z]]], {c, b1, 0, 1}], {b, a1, 0, 1}], {a, z1, 0, 1}], {z, 2, 3*5!}]; Union@lst (* Vladimir Joseph Stephan Orlovsky, Apr 11 2010 *)


CROSSREFS

Cf. A001235, A114923, A225908, A226903.
Sequence in context: A020938 A136360 A023483 * A128245 A117714 A245685
Adjacent sequences: A023039 A023040 A023041 * A023043 A023044 A023045


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



