%I A144293
%S A144293 1,1,2,5,5,13,29,877,23,53,4639,22619,2423,27644437,1800937,1101959,
%T A144293 43486067,255755771,5006399,222527,4326209287,188633,574631,13369534669,
%U A144293 1204457631577,171659,11759883224809,2479031,171572636187431,3516743833
%N A144293 Largest prime factor of n-th Bell number A000110(n) (or 1 if A000110(n) 
               = 1).
%C A144293 Contribution from David Pasino (davpas(AT)charter.net), Dec 03 2008: 
               (Start)
%C A144293 The number of refinements of a partition is the product of the Bell numbers 
               of the cell sizes.
%C A144293 The number of encoarsements is the Bell number of the number of cells.
%C A144293 For these to be equal, a Bell number has to be a product of Bell numbers.
%C A144293 This happens if there are n-1 single-element cells and 1 n-element cell.
%C A144293 Does it ever happen otherwise? (End)
%H A144293 T. D. Noe, <a href="b144293.txt">Table of n, a(n) for n = 0..70</a>
%H A144293 Simon Plouffe, <a href="http://www.lacim.uqam.ca/~plouffe/factors_of_bell_numbers.txt">
               Factors of Bell numbers</a> [From David Pasino (davpas(AT)charter.net), 
               Dec 03 2008]
%H A144293 Author?, <a href="http://www.prime-numbers.org/">rime number checker 
               up to 10000000000</a> [From David Pasino (davpas(AT)charter.net), 
               Dec 03 2008]
%Y A144293 Sequence in context: A100953 A112835 A154692 this_sequence A154694 A154696 
               A154698
%Y A144293 Adjacent sequences: A144290 A144291 A144292 this_sequence A144294 A144295 
               A144296
%K A144293 nonn
%O A144293 0,3
%A A144293 N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2008
%E A144293 a(15) - a(20) from David Pasino (davpas(AT)charter.net), Dec 03 2008
%E A144293 a(21) onwards from N. J. A. Sloane (njas(AT)research.att.com), Dec 04 
               2008
%E A144293 Corrected by David Pasino (davpas(AT)charter.net), Dec 14 2008