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A197181 Numbers that are a divisor of the product of the factorials of their digits in decimal representation.

%I A197181 #9 Jul 07 2019 14:31:11
%S A197181 1,2,3,4,5,6,7,8,9,15,16,18,24,28,36,45,48,60,64,70,72,75,80,84,90,96,
%T A197181 98,128,144,168,175,180,189,192,256,280,288,360,378,384,448,480,486,
%U A197181 567,576,588,640,648,672,675,720,729,756,768,784,840,864,875,882
%N A197181 Numbers that are a divisor of the product of the factorials of their digits in decimal representation.
%H A197181 Reinhard Zumkeller, <a href="/A197181/b197181.txt">Table of n, a(n) for n = 1..1000</a>
%e A197181 a(10)=15: A066459(15) = 1!*5! = 120 = 15 * 8;
%e A197181 a(11)=16: A066459(16) = 1!*6! = 720 = 16 * 45;
%e A197181 17 is not a term because 5040 mod 17 = 8, A066459(16) = 5040;
%e A197181 a(12)=18: A066459(15) = 1!*8! = 40320 = 18 * 2240.
%t A197181 Select[Range[900],IntegerQ[Times@@(IntegerDigits[#]!)/#]&] (* _Harvey P. Dale_, Jul 07 2019 *)
%o A197181 (Haskell)
%o A197181 import Data.List (elemIndices)
%o A197181 a197181 n = a197181_list !! (n-1)
%o A197181 a197181_list = map (+ 1) $ elemIndices 0 $
%o A197181    zipWith mod (map a066459 [1..]) [1..]
%Y A197181 Cf. A066459, A000142, A188264.
%K A197181 nonn,base
%O A197181 1,2
%A A197181 _Reinhard Zumkeller_, Oct 11 2011