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%I #13 Nov 21 2013 12:49:04
%S 793,15689,16354,117713,118378,133274,1771625,1772290,1787186,1889210,
%T 4826873,4827538,4842434,4944458,6598370,24137633,24138298,24153194,
%U 24255218,25909130,28964378,47045945,47046610,47061506,47163530
%N Numbers that are sums of sixth powers of two distinct primes.
%C This is to 6th powers as A130292 is to fifth powers, A130873 is to 4th powers and A120398 is to cubes. These can never be prime, as sixth powers are cubes and the sum of cubes factorizations applies. There are semiprimes for values beginning a(1) = 793, a(2) = 15689 = 29 * 541, a(4) = 117713 = 53 * 2221, a(11) = 4826873 = 173 * 27901.
%H Vincenzo Librandi, <a href="/A130555/b130555.txt">Table of n, a(n) for n = 1..8000</a>
%F {A001014(A000040(i)) + A001014(A000040(j)) for i > j}.
%e a(1) = prime(1)^6 + prime(2)^6 = 2^6 + 3^6 = 64 + 729 = 793 = 13 * 61.
%t Select[Sort[Flatten[Table[Prime[n]^6 + Prime[k]^6, {n, 15}, {k, n - 1}]]], # <= Prime[15^6] &]
%t Union[Total/@Subsets[Prime[Range[20]]^6,{2}]] (* _Harvey P. Dale_, Mar 11 2012 *)
%Y Cf. A000040, A001014, A050997, A120398, A122616, A130873.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Aug 09 2007