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 A112505 Number of primitive prime factors of 10^n-1. 8
 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 3, 3, 1, 1, 3, 2, 2, 3, 5, 3, 3, 5, 2, 3, 3, 1, 3, 1, 1, 2, 4, 3, 4, 3, 2, 4, 2, 1, 2, 3, 4, 2, 4, 2, 4, 2, 3, 2, 2, 3, 7, 1, 5, 4, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 4, 4, 6, 2, 5, 2, 3, 2, 3, 3, 3, 2, 5, 3, 7, 3, 1, 3, 5, 4, 3, 2, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Also the number of primes whose reciprocal is a repeating decimal of length n. The number of numbers in each row of table A046107. By Zsigmondy's theorem, a(n) >= 1. When a(n)=1, the corresponding prime is called a unique prime (see A007498, A040017 and A051627). LINKS Eric Weisstein's World of Mathematics, Primitive Prime Factor Eric Weisstein's World of Mathematics, Zsigmondy Theorem Eric Weisstein's World of Mathematics, Unique Prime MATHEMATICA pp={}; Table[f=Transpose[FactorInteger[10^n-1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Length[p], {n, 66}] CROSSREFS Cf. A007138 (smallest primitive prime factor of 10^n-1), A102347 (number of distinct prime factors of 10^n-1), A046107. Sequence in context: A156608 A323827 A275850 * A104638 A270648 A331034 Adjacent sequences: A112502 A112503 A112504 * A112506 A112507 A112508 KEYWORD hard,nonn AUTHOR T. D. Noe, Sep 08 2005 EXTENSIONS Terms to a(276) in b-file from T. D. Noe, Jun 01 2010 a(277)-a(322) in b-file from Ray Chandler, May 01 2017 a(323)-a(352) in b-file from Max Alekseyev, Apr 28 2022 STATUS approved

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Last modified November 28 00:05 EST 2022. Contains 358406 sequences. (Running on oeis4.)