OFFSET
1,1
COMMENTS
This is conjectured to be an infinite sequence.
Subsequence of A051302. [R. J. Mathar, Oct 14 2008]
First differs from A051302 at A051302(172)=3343221000 where 3343221000^2 = 279300^3 + 2234400^3 = 790020^3 + 2202480^3 = 1256850^3 + 2094750^3.
If n is a term of this sequence, then n^2 = a^3 + b^3 = c^3 + d^3 where (a, b) and (c, d) are distinct pairs. If n^2 = a^3 + b^3 = c^3 + d^3, then (n*k^3)^2 = n^2*k^6 = k^6*(a^3 + b^3) = k^6*(c^3 + d^3) = (a*k^2)^3 + (b*k^2)^3 = (c*k^2)^3 + (d*k^2)^3. It is obvious that if (a, b) and (c, d) are distinct, then (k^2*a, k^2*b), (k^2*c, k^2*d) are also distinct for all nonzero values of k. So if n is in this sequence and n*k^3 is not in A155961, then n*k^3 is in this sequence for all k > 0. If this sequence is not infinite, then there are infinitely many consecutive k values for any term n such that n*k^3 is in A155961. Is it possible? - Altug Alkan, May 10 2016
LINKS
Ray Chandler, Table of n, a(n) for n = 1..771
EXAMPLE
a(1): 77976^2 = 6080256576 = 1824^3 + 228^3 = 1710^3 + 1026^3;
a(2): 223587^2 = 49991146569 = 3666^3 + 897^3 = 3276^3 + 2457^3;
a(3): 623808^2 = 389136420864 = 7296^3 + 912^3 = 6840^3 + 4104^3;
a(4): 894348^2 = 799858345104 = 9282^3 + 546^3 = 9009^3 + 4095^3.
CROSSREFS
KEYWORD
nonn
AUTHOR
Iain Renfrew (iain.renfrew(AT)btinternet.com), Oct 13 2008
EXTENSIONS
a(5)-a(15) from Zak Seidov, Oct 15 2008
Extended by Ray Chandler, Nov 22 2011
STATUS
approved