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A060443 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), without repetition.

%I A060443 #31 Apr 18 2024 09:33:48
%S A060443 0,1,3,7,3,5,31,3,7,127,3,5,17,7,73,3,11,31,23,89,3,5,7,13,8191,3,43,
%T A060443 127,7,31,151,3,5,17,257,131071,3,7,19,73,524287,3,5,11,31,41,7,127,
%U A060443 337,3,23,89,683,47,178481,3,5,7,13,17,241
%N A060443 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), without repetition.
%C A060443 For n > 1, the length of row n is A046800(n). - _T. D. Noe_, Aug 06 2007
%D A060443 J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%H A060443 T. D. Noe, <a href="/A060443/b060443.txt">Rows n=0..500 of triangle, flattened</a> (derived from Brillhart et al.)
%H A060443 Joerg Arndt, <a href="/A001265/a001265.txt">Rows n=1..1200 of triangle when repetitions are included</a> (derived from Brillhart et al.)
%H A060443 J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A060443 Jeroen Demeyer, <a href="http://cage.ugent.be/~jdemeyer/cunningham/">Machine-readable Cunningham Tables</a> [Broken link]
%H A060443 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H A060443 Chai Wah Wu, <a href="https://github.com/postvakje/Reformatted-Cunningham-Project-tables">Tables from the Cunningham Project in machine-readable JSON format.</a>
%e A060443 From _Wolfdieter Lang_, Sep 23 2017: (Start)
%e A060443 The irregular triangle T(n,k) begins for n >= 2:
%e A060443 n\k      1   2    3    4   5
%e A060443 2:       3
%e A060443 3:       7
%e A060443 4:       3   5
%e A060443 5:      31
%e A060443 6:       3   7
%e A060443 7:     127
%e A060443 8:       3   5   17
%e A060443 9:       7  73
%e A060443 10:      3  11   31
%e A060443 11:     23  89
%e A060443 12:      3   5    7   13
%e A060443 13:   8191
%e A060443 14:      3  43  127
%e A060443 15:      7  31  151
%e A060443 16:      3   5   17  257
%e A060443 17: 131071
%e A060443 18:      3   7   19   73
%e A060443 19: 524287
%e A060443 20:      3   5   11   31  41
%e A060443 ... (End)
%t A060443 Array[FactorInteger[2^# - 1][[All, 1]] &, 25, 0] (* _Paolo Xausa_, Apr 18 2024 *)
%Y A060443 Cf. A001265, A064078.
%K A060443 nonn,tabf
%O A060443 0,3
%A A060443 _N. J. A. Sloane_