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Search: id:A132214
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| A132214 |
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Numbers that are sums of seventh powers of two distinct primes. |
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+0
5
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| 2315, 78253, 80312, 823671, 825730, 901668, 19487299, 19489358, 19565296, 20310714, 62748645, 62750704, 62826642, 63572060, 82235688, 410338801, 410340860, 410416798, 411162216, 429825844, 473087190, 893871867, 893873926
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OFFSET
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1,1
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COMMENT
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This is to 7th powers as A130555 is to 6th powers, A130292 is to fifth powers, A130873 is to 4th powers, and A120398 is to cubes. These can never be prime, as the polynomial x^7 + y^7 factors over Z. Note however that A132215, which is the analogue for eighth powers, can be prime, as seen also in A132216.
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FORMULA
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{A001015(A000040(i)) + A001015(A000040(j)) for i > j}.
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EXAMPLE
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a(1) = 2^7 + 3^7 = 2315 = 5 * 463.
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MATHEMATICA
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Select[Sort[ Flatten[Table[Prime[n]^7 + Prime[k]^7, {n, 15}, {k, n - 1}]]], # <= Prime[15^7] &]
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CROSSREFS
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Cf. A000040, A001015, A050997, A120398, A122616, A130873, A130555, A132215, A132216.
Sequence in context: A035893 A035771 A107567 this_sequence A133538 A075668 A137733
Adjacent sequences: A132211 A132212 A132213 this_sequence A132215 A132216 A132217
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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 13 2007
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