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A071869
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Numbers n such that Lpf(n) < Lpf(n+1) < Lpf(n+2) where Lpf(x) denotes the largest prime factor of x.
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12
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8, 9, 20, 21, 24, 27, 32, 45, 56, 57, 77, 81, 84, 90, 91, 92, 105, 114, 120, 125, 132, 135, 140, 144, 147, 165, 168, 169, 170, 171, 175, 176, 177, 189, 200, 204, 212, 216, 220, 221, 225, 231, 234, 235, 247, 252, 260, 261, 275, 288, 289, 300, 315, 324, 345, 354
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Erdos and Pomerance showed in 1978 that this sequence is infinite.
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REFERENCES
| Erdos P. and Pomerance C., "On the largest prime factors of n and n+1", Aequationes Math. vol. 17, 1978, p. 311-321
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = A079747(n+1) - 1. - T. D. Noe, Nov 26 2007
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PROG
| (PARI) for(n=2, 500, if(sign(component(component(factor(n), 1), omega(n))-component(component(factor(n+1), 1), omega(n+1)))+sign(component(component(factor(n+1), 1), omega(n+1))-component(component(factor(n+2), 1), omega(n+2)))==-2, print1(n, ", ")))
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CROSSREFS
| Cf. A006530, A070089.
Cf. A071870, A082417-A082422
Sequence in context: A022313 A120311 A061414 * A048124 A046258 A074344
Adjacent sequences: A071866 A071867 A071868 * A071870 A071871 A071872
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 09 2002
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