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

1,1

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

Links

Table of n, a(n) for n=1..21.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A266847 A345592 A345850 * A075669 A345602 A345861

Adjacent sequences: A132212 A132213 A132214 * A132216 A132217 A132218

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 13 2007

Status

approved