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

1,2

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.

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} ]

Crossrefs

Cf. A000110, A327432.

Sequence in context: A290631 A116693 A154565 * A073877 A248538 A248539

Adjacent sequences: A066559 A066560 A066561 * A066563 A066564 A066565

Keyword

nonn

Author

Amarnath Murthy, Dec 17 2001

Extensions

More terms from John W. Layman, Jan 02 2002

More terms from David Wasserman, Mar 31 2008

Status

approved