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A144293 Largest prime factor of n-th Bell number A000110(n) (or 1 if A000110(n) = 1). 4


%S 1,1,2,5,5,13,29,877,23,53,4639,22619,2423,27644437,1800937,1101959,

%T 43486067,255755771,5006399,222527,4326209287,188633,574631,

%U 13369534669,1204457631577,171659,11759883224809,2479031,171572636187431,3516743833

%N Largest prime factor of n-th Bell number A000110(n) (or 1 if A000110(n) = 1).

%C From _David Pasino_, Dec 03 2008: (Start)

%C The number of refinements of a partition is the product of the Bell numbers of the cell sizes.

%C The number of encoarsements is the Bell number of the number of cells.

%C For these to be equal, a Bell number has to be a product of Bell numbers.

%C This happens if there are n-1 single-element cells and 1 n-element cell.

%C Does it ever happen otherwise? (End)

%H Amiram Eldar, <a href="/A144293/b144293.txt">Table of n, a(n) for n = 0..104</a> (terms 0..70 from T. D. Noe)

%H Simon Plouffe, <a href="http://plouffe.fr/simon/constants/factors_of_bell_numbers.txt">Factors of Bell numbers</a> [_David Pasino_, Dec 03 2008]

%H Prime-Numbers.org, <a href="http://www.prime-numbers.org/">Prime number checker up to 10000000000</a> [_David Pasino_, Dec 03 2008]

%t Join[{1}, Table[FactorInteger[BellB[n]][[-1, 1]], {n, 40}]] (* _Vincenzo Librandi_, Jan 04 2017 *)

%o (MAGMA) [1,1] cat [Maximum(PrimeDivisors(Bell(n))): n in [2..30]]; // _Vincenzo Librandi_, Jan 04 2017

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Dec 03 2008

%E a(15)-a(20) from _David Pasino_, Dec 03 2008

%E a(21) onwards from _N. J. A. Sloane_, Dec 04 2008

%E Corrected by _David Pasino_, Dec 14 2008

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Last modified May 12 23:35 EDT 2021. Contains 343829 sequences. (Running on oeis4.)