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A023503
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Greatest prime divisor of prime(n) - 1.
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10
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2, 2, 3, 5, 3, 2, 3, 11, 7, 5, 3, 5, 7, 23, 13, 29, 5, 11, 7, 3, 13, 41, 11, 3, 5, 17, 53, 3, 7, 7, 13, 17, 23, 37, 5, 13, 3, 83, 43, 89, 5, 19, 3, 7, 11, 7, 37, 113, 19, 29, 17, 5, 5, 2, 131, 67, 5, 23, 7, 47, 73, 17, 31, 13, 79, 11, 7, 173, 29, 11, 179, 61, 31, 7, 191
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Baker & Harman (1998) show that there are infinitely many n such that a(n) > prime(n)^0.677. This improves on earlier work of Goldfeld, Hooley, Fouvry, Deshouillers, Iwaniec, Motohashi, et al.
Fouvry shows that a(n) > prime(n)^0.6683 for a positive proportion of members of this sequence. See Fouvry and also Baker & Harman (1996) which corrected an error in the former work.
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REFERENCES
| R. C. Baker and G. Harman, The Brun-Titchmarsh theorem on average, Analytic Number Theory (Proceedings in honor of Heini Halberstam), Birkhauser, Boston, 1996, pp. 39-103.
Etienne Fouvry, "Théorème de Brun-Titchmarsh; application au théorème de Fermat". Invent. Math 79 (1985), 383-407.
D. M. Goldfeld, "On the number of primes p for which p + a has a large prime factor". Mathematika 16 (1969), pp. 23-27.
R. R. Hall, Some properties of the sequence {p-1}. Acta Arith. 28 (1975/76), 101-105.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 2..10000
R. Baker and G. Harman, Shifted primes without large prime factors, Acta Arithmetica 83 (1998), pp. 331-361.
G. Harman, On the greatest prime factor of p-1 with effective constants
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MAPLE
| s1:=[]; for n from 2 to 120 do m:=ithprime(n)-1; t1:=ifactors(m); t2:=t1[2][nops(t1[2])]; s1:=[op(s1), t2[1]]; od: s1; # assumes ifactors returns the prime factors in increasing order, but I am not certain this is correct
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MATHEMATICA
| Table[FactorInteger[Prime[n] - 1][[-1, 1]], {n, 2, 100}] (* T. D. Noe, Jun 08 2011 *)
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CROSSREFS
| Sequence in context: A203955 A039638 A090926 * A039640 A053811 A049840
Adjacent sequences: A023500 A023501 A023502 * A023504 A023505 A023506
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Comments, references, and links from Charles R Greathouse IV, Mar 04, 2011
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