

A144293


Largest prime factor of nth 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
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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 n1 singleelement cells and 1 nelement 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]
PrimeNumbers.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
Adjacent sequences: A144290 A144291 A144292 * A144294 A144295 A144296


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



