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

1,1

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.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A107567 A238025 A369960 * A133538 A075668 A210175

Adjacent sequences: A132211 A132212 A132213 * A132215 A132216 A132217

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 13 2007

Status

approved