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Sorted prime signature of 2^n - 1.
7

%I #6 May 13 2019 08:12:41

%S 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,3,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1

%N Sorted prime signature of 2^n - 1.

%C The sorted prime signature of n is row n of A124010.

%e We have 2^126 - 1 = 3^3 * 7^2 * 19 * 43 * 73 * 127 * 337 * 5419 * 92737 * 649657 * 77158673929, so row n = 126 is {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3}.

%e Triangle begins:

%e 1

%e 1

%e 1

%e 1 1

%e 1

%e 1 2

%e 1

%e 1 1 1

%e 1 1

%e 1 1 1

%e 1 1

%e 1 1 1 2

%e 1

%e 1 1 1

%e 1 1 1

%e 1 1 1 1

%e 1

%e 1 1 1 3

%e 1

%e 1 1 1 1 2

%t Table[Sort[Last/@FactorInteger[2^n-1]],{n,30}]

%Y Cf. A001222, A056239, A067255, A071625, A112798, A118914, A124010.

%Y Mersenne numbers: A046051, A046800, A059305, A325610, A325611, A325612.

%K nonn,tabf

%O 1,8

%A _Gus Wiseman_, May 13 2019