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

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, 98, 128, 144, 168, 175, 180, 189, 192, 256, 280, 288, 360, 378, 384, 448, 480, 486, 567, 576, 588, 640, 648, 672, 675, 720, 729, 756, 768, 784, 840, 864, 875, 882

Offset: 1

Author

Reinhard Zumkeller, Oct 11 2011

Keywords

• nonn
• base

Examples

			a(10)=15: A066459(15) = 1!*5! = 120 = 15 * 8;
a(11)=16: A066459(16) = 1!*6! = 720 = 16 * 45;
17 is not a term because 5040 mod 17 = 8, A066459(16) = 5040;
a(12)=18: A066459(15) = 1!*8! = 40320 = 18 * 2240.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066459, A000142, A188264.

Programs

Haskell

import Data.List (elemIndices)
a197181 n = a197181_list !! (n-1)
a197181_list = map (+ 1) $ elemIndices 0 $
   zipWith mod (map a066459 [1..]) [1..]

Mathematica

Select[Range[900],IntegerQ[Times@@(IntegerDigits[#]!)/#]&] (* Harvey P. Dale, Jul 07 2019 *)