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A001265 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.

%I A001265 #51 Feb 16 2025 08:32:23
%S A001265 3,7,3,5,31,3,3,7,127,3,5,17,7,73,3,11,31,23,89,3,3,5,7,13,8191,3,43,
%T A001265 127,7,31,151,3,5,17,257,131071,3,3,3,7,19,73,524287,3,5,5,11,31,41,7,
%U A001265 7,127,337,3,23,89,683,47,178481,3,3,5,7,13,17,241
%N A001265 Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.
%C A001265 For n > 1, the length of row n is A046051(n). - _T. D. Noe_, Aug 06 2007
%D A001265 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 A001265 Max Alekseyev, <a href="/A001265/b001265.txt">Rows n = 2..1206, flattened</a> (rows 2..500 from T. D. Noe)
%H A001265 Joerg Arndt, <a href="/A001265/a001265_1.txt">Rows n = 1..1200 of triangle</a> (derived from Brillhart et al.; updated by Jon E. Schoenfield)
%H A001265 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 A001265 Jeroen Demeyer, <a href="http://cage.ugent.be/~jdemeyer/cunningham/">Machine-readable Cunningham Tables</a>
%H A001265 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H A001265 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>
%H A001265 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 A001265 Table begins:
%e A001265  n=2: 3;
%e A001265  n=3: 7;
%e A001265  n=4: 3, 5;
%e A001265  n=5: 31;
%e A001265  n=6: 3, 3, 7;
%e A001265  n=7: 127;
%e A001265  n=8: 3, 5, 17;
%e A001265   ...
%t A001265 Array[Flatten[ConstantArray[#1, #2] & @@ # & /@ FactorInteger[2^# - 1]] &, 24] // Flatten (* _Michael De Vlieger_, Dec 04 2017 *)
%o A001265 (PARI) row(n)= if (n==1, return ([0])); my(f = factor(2^n-1), v = []); for (i=1, #f~, for (j=1, f[i, 2], v = concat(v, f[i,j]))); v; \\ _Michel Marcus_, Dec 05 2017
%Y A001265 Cf. A060443, A182590.
%K A001265 nonn,tabf
%O A001265 2,1
%A A001265 _N. J. A. Sloane_
%E A001265 Ambiguous rows 0 and 1 removed by _Max Alekseyev_, Jul 25 2023