A132214 Numbers that are sums of seventh powers of two distinct primes.

2315, 78253, 80312, 823671, 825730, 901668, 19487299, 19489358, 19565296, 20310714, 62748645, 62750704, 62826642, 63572060, 82235688, 410338801, 410340860, 410416798, 411162216, 429825844, 473087190, 893871867, 893873926

Offset: 1

Author

Jonathan Vos Post, Aug 13 2007

Keywords

• easy
• nonn

Comments

This is to 7th powers as A130555 is to 6th powers, A130292 is to fifth powers, A130873 is to 4th powers and A120398 is to cubes. These can never be prime, as the polynomial x^7 + y^7 factors over Z. Note however that A132215, which is the analog for eighth powers, can be prime, as seen also in A132216.

Examples

			a(1) = 2^7 + 3^7 = 2315 = 5 * 463.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001015, A050997, A120398, A122616, A130873, A130555, A132215, A132216.

Programs

Maple

P:= select(isprime, [2,seq(i,i=3..100,2)]): nP:= nops(P):
N:= 2^7 + P[-1]^7:
sort(convert(select(`<=`, {seq(seq(P[i]^7+P[j]^7,j=i+1..nP),i=1..nP-1)},N),list)); # Robert Israel, Jul 01 2024

Mathematica

Select[Sort[ Flatten[Table[Prime[n]^7 + Prime[k]^7, {n, 15}, {k, n - 1}]]], # <= Prime[15^7] &]
Union[Total/@(Subsets[Prime[Range[10]],{2}]^7)] (* Harvey P. Dale, Jan 03 2012 *)

Formula

{A001015(A000040(i)) + A001015(A000040(j)) for i > j}.