A132214 - OEIS

%I #14 Jul 02 2024 02:14:12

%S 2315,78253,80312,823671,825730,901668,19487299,19489358,19565296,

%T 20310714,62748645,62750704,62826642,63572060,82235688,410338801,

%U 410340860,410416798,411162216,429825844,473087190,893871867,893873926

%N Numbers that are sums of seventh powers of two distinct primes.

%C 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.

%H Robert Israel, <a href="/A132214/b132214.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p P:= select(isprime, [2,seq(i,i=3..100,2)]): nP:= nops(P):

%p N:= 2^7 + P[-1]^7:

%p 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

%t Select[Sort[ Flatten[Table[Prime[n]^7 + Prime[k]^7, {n, 15}, {k, n - 1}]]], # <= Prime[15^7] &]

%t Union[Total/@(Subsets[Prime[Range[10]],{2}]^7)] (* _Harvey P. Dale_, Jan 03 2012 *)

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

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 13 2007