login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A023042 Numbers whose cube is the sum of three distinct nonnegative cubes. 8
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

REFERENCES

Ya. I. Perelman, Algebra can be fun, pp. 142-143.

LINKS

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

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[y<x, Break[], If[y==x, AppendTo[lst, z]]], {c, b-1, 0, -1}], {b, a-1, 0, -1}], {a, z-1, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 04:27 EST 2016. Contains 278902 sequences.