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Search: id:A130555
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| A130555 |
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Numbers that are sums of sixth powers of two distinct primes. |
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+0
6
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| 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
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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{A001014(A000040(i)) + A001014(A000040(j)) for i > j}.
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EXAMPLE
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a(1) = prime(1)^6 + prime(2)^6 = 2^6 + 3^6 = 64 + 729 = 793 = 13 * 61.
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MATHEMATICA
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Select[Sort[Flatten[Table[Prime[n]^6 + Prime[k]^6, {n, 15}, {k, n - 1}]]], # <= Prime[15^6] &]
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CROSSREFS
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Cf. A000040, A001014, A050997, A120398, A122616, A130873.
Sequence in context: A037146 A045246 A095812 this_sequence A133537 A075667 A136543
Adjacent sequences: A130552 A130553 A130554 this_sequence A130556 A130557 A130558
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Aug 09 2007
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