A281789 - OEIS

%I #8 Feb 08 2017 02:05:24

%S 9,144,577,729,1010,2304,3097,3753,5625,11664,21609,36864,51762,59049,

%T 90000,131769,186624,243876,257049,345744,455625,589824,713337,751689,

%U 826809,944784,1172889,1440000,1613673,1750329,2108304,2518569,2985984,3132585,3515625

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

%C 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.

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

%H Chai Wah Wu, <a href="/A281789/b281789.txt">Table of n, a(n) for n = 1..44</a>

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

%K nonn

%O 1,1

%A _Chai Wah Wu_, Jan 31 2017