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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 (list; graph; refs; listen; history; text; internal format)
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

T. D. Noe, Table of n, a(n) for n = 0..70

Simon Plouffe, Factors of Bell numbers [David Pasino, Dec 03 2008]

Author?, 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: A222114 A303355 A154692 * 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

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Last modified October 22 21:09 EDT 2018. Contains 316505 sequences. (Running on oeis4.)