A132215 Numbers that are sums of eighth powers of two distinct primes.

6817, 390881, 397186, 5765057, 5771362, 6155426, 214359137, 214365442, 214749506, 220123682, 815730977, 815737282, 816121346, 821495522, 1030089602, 6975757697, 6975764002, 6976148066, 6981522242, 7190116322, 7791488162

Offset: 1

Author

Jonathan Vos Post, Aug 13 2007

Keywords

• easy
• nonn

Comments

This is to 8th powers as A132214 is to 7th powers, A130555 is to 6th powers, A130292 is to fifth powers, A130873 is to 4th powers and A120398 is to cubes. These CAN be prime, as the polynomial x^8 + y^8 is irreducible over Z, as seen in A132216. The first such example is a(11) = A132216(1) = 2^8 + 13^8 = 256 + 815730721 = 815730977, which is prime.

A subset of A003380. - R. J. Mathar, May 11 2008

Examples

			a(1) = 2^8 + 3^8 = 256 + 6561 = 6817 = 17 * 401.
		

Crossrefs

Cf. A000040, A001016, A050997, A120398, A122616, A130873, A130555, A132214, A132216.

Programs

Mathematica

Select[Sort[ Flatten[Table[Prime[n]^8 + Prime[k]^8, {n, 15}, {k, n - 1}]]], # <= Prime[15^8] &]
Total/@Subsets[Prime[Range[10]]^8,{2}]//Sort (* Harvey P. Dale, Jun 27 2017 *)

Formula

{A001016(A000040(i)) + A001016(A000040(j)) for i > j}.