This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112505 #16 Feb 16 2025 08:32:59
%S A112505 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,
%T A112505 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,
%U A112505 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
%N A112505 Number of primitive prime factors of 10^n-1.
%C A112505 Also the number of primes whose reciprocal is a repeating decimal of length n. The number of numbers in each row of table A046107.
%C A112505 By Zsigmondy's theorem, a(n) >= 1. When a(n)=1, the corresponding prime is called a unique prime (see A007498, A040017 and A051627).
%H A112505 <a href="/A112505/b112505.txt">Table of n, a(n) for n = 1..352</a>
%H A112505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimitivePrimeFactor.html">Primitive Prime Factor</a>
%H A112505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ZsigmondyTheorem.html">Zsigmondy Theorem</a>
%H A112505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UniquePrime.html">Unique Prime</a>
%t A112505 pp={}; Table[f=Transpose[FactorInteger[10^n-1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Length[p], {n, 66}]
%Y A112505 Cf. A007138 (smallest primitive prime factor of 10^n-1), A102347 (number of distinct prime factors of 10^n-1), A046107.
%K A112505 hard,nonn
%O A112505 1,5
%A A112505 _T. D. Noe_, Sep 08 2005
%E A112505 Terms to a(276) in b-file from _T. D. Noe_, Jun 01 2010
%E A112505 a(277)-a(322) in b-file from _Ray Chandler_, May 01 2017
%E A112505 a(323)-a(352) in b-file from _Max Alekseyev_, Apr 28 2022