

A112505


Number of primitive prime factors of 10^n1.


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
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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^n1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Length[p], {n, 66}]


CROSSREFS

Cf. A007138 (smallest primitive prime factor of 10^n1), A102347 (number of distinct prime factors of 10^n1), 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 bfile from T. D. Noe, Jun 01 2010
a(277)a(322) in bfile from Ray Chandler, May 01 2017
a(323)a(352) in bfile from Max Alekseyev, Apr 28 2022


STATUS

approved



