cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A130555 Numbers that are sums of sixth powers of two distinct primes.

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%I A130555 #13 Nov 21 2013 12:49:04
%S A130555 793,15689,16354,117713,118378,133274,1771625,1772290,1787186,1889210,
%T A130555 4826873,4827538,4842434,4944458,6598370,24137633,24138298,24153194,
%U A130555 24255218,25909130,28964378,47045945,47046610,47061506,47163530
%N A130555 Numbers that are sums of sixth powers of two distinct primes.
%C A130555 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 A130555 Vincenzo Librandi, <a href="/A130555/b130555.txt">Table of n, a(n) for n = 1..8000</a>
%F A130555 {A001014(A000040(i)) + A001014(A000040(j)) for i > j}.
%e A130555 a(1) = prime(1)^6 + prime(2)^6 = 2^6 + 3^6 = 64 + 729 = 793 = 13 * 61.
%t A130555 Select[Sort[Flatten[Table[Prime[n]^6 + Prime[k]^6, {n, 15}, {k, n - 1}]]], # <= Prime[15^6] &]
%t A130555 Union[Total/@Subsets[Prime[Range[20]]^6,{2}]] (* _Harvey P. Dale_, Mar 11 2012 *)
%Y A130555 Cf. A000040, A001014, A050997, A120398, A122616, A130873.
%K A130555 easy,nonn
%O A130555 1,1
%A A130555 _Jonathan Vos Post_, Aug 09 2007