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A112505
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Number of primitive prime factors of 10^n-1.
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7
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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; internal format)
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OFFSET
| 1,5
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..276
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
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MATHEMATICA
| pp={}; Table[f=Transpose[FactorInteger[10^n-1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Length[p], {n, 66}]
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CROSSREFS
| Cf. A007138 (smallest primitive prime factor of 10^n-1), A102347 (number of distinct prime factors of 10^n-1).
Sequence in context: A037805 A106825 A156608 * A104638 A057155 A037812
Adjacent sequences: A112502 A112503 A112504 * A112506 A112507 A112508
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KEYWORD
| hard,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 08 2005
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