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

793, 15689, 16354, 117713, 118378, 133274, 1771625, 1772290, 1787186, 1889210, 4826873, 4827538, 4842434, 4944458, 6598370, 24137633, 24138298, 24153194, 24255218, 25909130, 28964378, 47045945, 47046610, 47061506, 47163530

Offset: 1

Author

Jonathan Vos Post, Aug 09 2007

Keywords

• easy
• nonn

Comments

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.

Examples

			a(1) = prime(1)^6 + prime(2)^6 = 2^6 + 3^6 = 64 + 729 = 793 = 13 * 61.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8000

Crossrefs

Cf. A000040, A001014, A050997, A120398, A122616, A130873.

Programs

Mathematica

Select[Sort[Flatten[Table[Prime[n]^6 + Prime[k]^6, {n, 15}, {k, n - 1}]]], # <= Prime[15^6] &]
Union[Total/@Subsets[Prime[Range[20]]^6,{2}]] (* Harvey P. Dale, Mar 11 2012 *)

Formula

{A001014(A000040(i)) + A001014(A000040(j)) for i > j}.