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%I #38 Apr 26 2022 18:50:13
%S 0,1,2,2,2,5,2,4,3,4,2,7,3,4,6,6,2,8,1,7,7,6,1,10,5,6,5,8,5,13,3,11,6,
%T 6,7,11,3,3,6,11,4,14,4,10,9,6,2,13,4,10,8,9,4,12,8,12,6,8,2,20,7,5,
%U 13,15,7,14,3,10,6,12,2,17,3,7,12,6,8,15,6,15,10,7,3,21,7,8,10,14,5,21,12,10
%N Number of distinct prime factors of the repunit (-1 + 10^n)/9.
%C Factoring certain repunits is especially difficult.
%D Yates, S. "Peculiar Properties of Repunits." J. Recr. Math. 2, 139-146,1969.
%D Yates, S. "Prime Divisors of Repunits." J. Recr. Math. 8, 33-38, 1975.
%H <a href="/A095370/b095370.txt">Table of n, a(n) for n = 1..352</a>
%H P. De Geest, <a href="http://www.worldofnumbers.com/repunits.htm">Repunits and their prime factors</a>
%H T. Granlund, <a href="http://www.swox.com/gmp/repunit.html">Repunits.</a>
%H M. Kamada, <a href="https://stdkmd.net/nrr/repunit/">Factorization of 11...11(Repunits)</a>
%H Y. Koide, <a href="http://www.h4.dion.ne.jp/~rep">Factorization of Repunit Numbers</a>
%H W. M. Snyder, <a href="http://www.jstor.org/stable/2321382">Factoring Repunits</a>, Am. Math. Monthly 89, 462-466, 1982.
%H P. Yiu, <a href="http://math.fau.edu/yiu/RecreationalMathematics2003.pdf">Factorizations of repunits R_n for n<=50</a> Appendix Chap.18.5 pp. 173/360 in 'Recreational Mathematics'
%F a(n) = A001221(A002275(n)).
%F If 3|n, then a(n) = A102347(n); otherwise a(n) = A102347(n) - 1. - _Max Alekseyev_, Apr 25 2022
%e a(62)=5 because
%e 11111111111111111111111111111111111111111111111111111111111111 =
%e 11 * 2791 * 6943319 * 57336415063790604359 * 909090909090909090909090909091.
%e a(97)=3 because (10^97 - 1)/9 = 12004721 * 846035731396919233767211537899097169 * 109399846855370537540339266842070119107662296580348039.
%t lst={};Do[p=(10^n-1)/9;AppendTo[lst,Length[FactorInteger[p]]],{n,0,2*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 15 2009 *)
%o (PARI) a(n)=omega(10^n\9) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A067063, A003020, A001221, A002275, A095371.
%Y Cf. A046053 (total number of prime factors).
%K nonn
%O 1,3
%A _Labos Elemer_, Jun 04 2004; corrected Jun 09 2004
%E Terms to a(322) in b-file from _Ray Chandler_, Apr 22 2017
%E a(323)-a(352) in b-file from _Max Alekseyev_, Apr 26 2022
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