Search: id:A095370
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%I A095370
%S A095370 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,
               6,
%T A095370 7,11,3,3,6,11,4,14,4,10,9,6,2,13,4,10,8,9,4,12,8,12,6,8,2,20,7,5,13,15,
%U A095370 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 A095370 Number of distinct prime factors of the repunit (-1+10^n)/9.
%C A095370 Factoring certain repunits is especially difficult.
%D A095370 Snyder, W. M. "Factoring Repunits." Am. Math. Monthly 89, 462-466, 1982.
%D A095370 Yates, S. "Peculiar Properties of Repunits." J. Recr. Math. 2, 139-146,
               1969.
%D A095370 Yates, S. "Prime Divisors of Repunits." J. Recr. Math. 8, 33-38, 1975.
%H A095370 P. De Geest, <a href="http://www.worldofnumbers.com/repunits.htm">Repunits 
               and their prime factors</a>
%H A095370 T. Granlund, <a href="http://www.swox.com/gmp/repunit.html">Repunits.</
               a>
%H A095370 M. Kamada, <a href="http://homepage2.nifty.com/m_kamada/math/11111.htm">
               Factorization of 11...11(Repunits)</a>
%H A095370 Y. Koide, <a href="http://www.h4.dion.ne.jp/~rep">Factorization of Repunit 
               Numbers</a>
%H A095370 P. Yiu, <a href="http://www.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 A095370 a[n]=A001221[A002275(n)]
%e A095370 a[62]=5 because
%e A095370 11111111111111111111111111111111111111111111111111111111111111=
%e A095370 11*2791*6943319*57336415063790604359*909090909090909090909090909091
%e A095370 a[97]=3 because (10^97-1)/9=12004721*846035731396919233767211537899097169*10939984685537053754033926684207011\
               9107662296580348039.
%t A095370 lst={};Do[p=(10^n-1)/9;AppendTo[lst,Length[FactorInteger[p]]],{n,0,2*4!}];
               lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009]
%Y A095370 Cf. A067063, A003020, A001221, A002275, A094371.
%Y A095370 Cf. A046053 (total number of prime factors).
%Y A095370 Sequence in context: A130155 A113516 A120642 this_sequence A046053 A080348 
               A096396
%Y A095370 Adjacent sequences: A095367 A095368 A095369 this_sequence A095371 A095372 
               A095373
%K A095370 nonn
%O A095370 1,3
%A A095370 Labos E. (labos(AT)ana.sote.hu), Jun 04 2004; corrected Jun 09 2004

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