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