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A144293
Largest prime factor of n-th Bell number A000110(n) (or 1 if A000110(n) = 1).
4
1, 1, 2, 5, 5, 13, 29, 877, 23, 53, 4639, 22619, 2423, 27644437, 1800937, 1101959, 43486067, 255755771, 5006399, 222527, 4326209287, 188633, 574631, 13369534669, 1204457631577, 171659, 11759883224809, 2479031, 171572636187431, 3516743833
OFFSET
0,3
COMMENTS
From David Pasino, Dec 03 2008: (Start)
The number of refinements of a partition is the product of the Bell numbers of the cell sizes.
The number of encoarsements is the Bell number of the number of cells.
For these to be equal, a Bell number has to be a product of Bell numbers.
This happens if there are n-1 single-element cells and 1 n-element cell.
Does it ever happen otherwise? (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..104 (terms 0..70 from T. D. Noe)
Simon Plouffe, Factors of Bell numbers [David Pasino, Dec 03 2008]
Prime-Numbers.org, Prime number checker up to 10000000000 [David Pasino, Dec 03 2008]
MATHEMATICA
Join[{1}, Table[FactorInteger[BellB[n]][[-1, 1]], {n, 40}]] (* Vincenzo Librandi, Jan 04 2017 *)
PROG
(Magma) [1, 1] cat [Maximum(PrimeDivisors(Bell(n))): n in [2..30]]; // Vincenzo Librandi, Jan 04 2017
CROSSREFS
Sequence in context: A303355 A154692 A309161 * A174098 A183419 A305314
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 03 2008
EXTENSIONS
a(15)-a(20) from David Pasino, Dec 03 2008
a(21) onwards from N. J. A. Sloane, Dec 04 2008
Corrected by David Pasino, Dec 14 2008
STATUS
approved