A066562 Smallest Bell number (A000110) divisible by n, if such a number exists, otherwise 0.

1, 2, 15, 52, 5, 4140, 203, 0, 4140, 4140, 10293358946226376485095653, 4140, 52, 51724158235372, 15, 0, 4506715738447323, 4140, 21147, 4140, 21147, 1052928518014714166107781298021583534928402714242132, 4140, 0, 115975, 52, 82864869804, 51724158235372, 203, 4140

Offset: 1

Author

Amarnath Murthy, Dec 17 2001

Keywords

• nonn

Comments

No Bell number is divisible by 8. - John W. Layman, Jan 02 2002

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..134
• J. W. Layman, Maximum zero strings of Bell numbers modulo primes, J. Comb. Th. A40 (1985),161-168.
• G. T. Williams, Numbers generated by the function e^(e^x-1), Am. Math. Monthly 52 (1945),323-327.

Crossrefs

Cf. A000110, A327432.

Programs

Mathematica

b[ n_ ] := Nest[ Factor[ D[ #1, x ] ] &, Exp[ Exp[ x - 1 ] - 1 ], n ] /. (x -> 1); Do[ k = 1; While[ c = b[ k ]; !IntegerQ[ c/n ], k++ ]; Print[ c ], {n, 1, 7} ]

Extensions

More terms from John W. Layman, Jan 02 2002

More terms from David Wasserman, Mar 31 2008