A281789 Numbers n such that n^3-1 is a sum of cubes in 1 way and a difference of cubes in 2 ways.

9, 144, 577, 729, 1010, 2304, 3097, 3753, 5625, 11664, 21609, 36864, 51762, 59049, 90000, 131769, 186624, 243876, 257049, 345744, 455625, 589824, 713337, 751689, 826809, 944784, 1172889, 1440000, 1613673, 1750329, 2108304, 2518569, 2985984, 3132585, 3515625

Offset

1,1

Comments

By Fermat's Last Theorem, n^3 cannot be the difference nor the sum of 2 positive cubes, but n^3+1 or n^3-1 could be. If n^3-1 is also the sum of positive cubes and the difference of two other positives cubes besides n^3 and 1^3, then n is a term of the sequence. Interestingly, I have not been able to find numbers n such that n^3+1 is a difference of 2 positive cubes in 1 way and the sum of 2 positive cubes in 2 ways.

Conjecture: if a term n is square, then 10000*n is also a term.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..44

Example

3515625 is a term since 3515625^3 - 1 = 140624^3 + 3515550^3 = 3515700^3 - 140626^3.

Crossrefs

Sequence in context: A317354 A050787 A017198 * A134176 A325173 A067415

Adjacent sequences: A281786 A281787 A281788 * A281790 A281791 A281792

Keyword

nonn

Author

Chai Wah Wu, Jan 31 2017

Status

approved