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%I #6 Aug 09 2015 00:38:06
%S 1,2,6,24,120,6,5040,40320,362880,720,39916800,479001600,6227020800,
%T 87178291200,1307674368000,20922789888000,355687428096000,
%U 6402373705728000,121645100408832000,2432902008176640000
%N Least factorial obtained as n(n-1)...(n-k).
%C Max (a(n)) = n!. a(n!) = n!. Define numbers of the type 10 as factoriable numbers. Are there any more such numbers? i.e. numbers of the type k such that a(k) is neither k nor k!.
%e a(10) = 10*9*8 = 720.
%e a(6) = 6.
%p isfact := proc(n) local i ; for i from 1 do if i! = n then RETURN(true) ; elif i! > n then RETURN(false) ; fi ; od; end: A110808 := proc(n) local k,nfall ; for k from 0 do nfall := mul(n-i,i=0..k) ; if isfact(nfall) then RETURN(nfall) ; fi ; od: end: seq(A110808(n),n=1..40) ; # _R. J. Mathar_, Feb 08 2008
%K nonn
%O 1,2
%A _Amarnath Murthy_, Aug 14 2005
%E More terms from _R. J. Mathar_, Feb 08 2008
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