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

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

Author

N. J. A. Sloane, Dec 03 2008

Keywords

• nonn

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]

Programs

Magma

[1,1] cat [Maximum(PrimeDivisors(Bell(n))): n in [2..30]]; // Vincenzo Librandi, Jan 04 2017

Mathematica

Join[{1}, Table[FactorInteger[BellB[n]][[-1, 1]], {n, 40}]] (* Vincenzo Librandi, Jan 04 2017 *)

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