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%I #11 Sep 10 2019 07:30:41
%S 1,2,15,52,5,4140,203,0,4140,4140,10293358946226376485095653,4140,52,
%T 51724158235372,15,0,4506715738447323,4140,21147,4140,21147,
%U 1052928518014714166107781298021583534928402714242132,4140,0,115975,52,82864869804,51724158235372,203,4140
%N Smallest Bell number (A000110) divisible by n, if such a number exists, otherwise 0.
%C No Bell number is divisible by 8. - _John W. Layman_, Jan 02 2002
%H Vaclav Kotesovec, <a href="/A066562/b066562.txt">Table of n, a(n) for n = 1..134</a>
%H J. W. Layman, <a href="https://doi.org/10.1016/0097-3165(85)90055-X">Maximum zero strings of Bell numbers modulo primes</a>, J. Comb. Th. A40 (1985),161-168.
%H G. T. Williams, <a href="http://www.jstor.org/stable/2305292">Numbers generated by the function e^(e^x-1)</a>, Am. Math. Monthly 52 (1945),323-327.
%t 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} ]
%Y Cf. A000110, A327432.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Dec 17 2001
%E More terms from _John W. Layman_, Jan 02 2002
%E More terms from _David Wasserman_, Mar 31 2008
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