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Search: id:A109314
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| A109314 |
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Numbers n such that prime(n) + n is a prime power. |
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+0
1
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| 3, 5, 8, 9, 12, 86, 230, 503, 1170, 2660, 2772, 6288, 6572, 8858, 9590, 14870, 16332, 17708, 53132, 54540, 63890, 64908, 82830, 93068, 98132, 104726, 119298, 136502, 152198, 177918, 187040, 234650, 241682, 253118, 263930, 278970, 376680, 412440
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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prime(n) + n = q^k, q is prime and k_Integer >= 2.
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EXAMPLE
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2660 is OK because prime(2660)+2660=23909+2660=26569=1632, 163 is prime.
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MATHEMATICA
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lst = {}; fQ[n_] := Block[{pf = FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] + n], Print[n]; AppendTo[lst, n]], {n, 456109}]; lst
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CROSSREFS
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Cf. A025475 = powers of a prime but not prime, also nonprime n such that sigma(n)*phi(n)>(n-1)2; A107708 = values of q, A107709 = values of k; A107710 = values of prime (A109314(n)).
Sequence in context: A051206 A081451 A107605 this_sequence A102529 A002159 A050094
Adjacent sequences: A109311 A109312 A109313 this_sequence A109315 A109316 A109317
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 25 2005
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