A333880 Number of integer solutions to n = x^k - y^k with x > y >= 0 and k >= 2.

0, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 1, 0, 3, 3, 1, 0, 2, 1, 2, 0, 1, 2, 2, 1, 3, 1, 1, 0, 2, 3, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 1, 1, 3, 0, 1, 3, 2, 0, 2, 1, 1, 0, 2, 3, 2, 0, 1, 2, 2, 0, 5, 5, 3, 0, 1, 1, 2, 0, 1, 3, 1, 0, 3, 1, 2, 0, 1, 4, 4, 0, 1, 2, 2, 0, 2, 2

Offset: 2

Author

Peter Kagey, Apr 08 2020

Keywords

• nonn

Comments

a(n) = 0 for all n in A303744.

Records occur at n = 2, 3, 7, 15, 63, 240, 480, 720, 960, 1440, 2400, 2880, 3360, 4032, 5040, ... - Peter Kagey, Nov 18 2020

Examples

			For n = 63, the a(63) = 5 solutions are
   8^2 -  1^2 =   64 -   1,
  12^2 -  9^2 =  144 -  81,
  32^2 - 31^2 = 1024 - 961,
   4^3 -  1^3 =   64 -   1, and
   2^6 -  1^6 =   64 -   1.
		

Links

• Peter Kagey, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A034178, A303744, A333822, A333868.