The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A112505 Number of primitive prime factors of 10^n-1. 9
 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 Table of n, a(n) for n = 1..352 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: A368752 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 11:49 EDT 2024. Contains 372940 sequences. (Running on oeis4.)