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

1,1

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.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A045246 A095812 A212239 * A133537 A213471 A075667

Adjacent sequences: A130552 A130553 A130554 * A130556 A130557 A130558

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 09 2007

Status

approved