A197181 -id:A197181 - cp's OEIS frontend

A188264 Numbers m that are divisible by the product of the factorials of their digits in base 10.

1, 2, 10, 11, 12, 20, 30, 100, 101, 102, 110, 111, 112, 120, 132, 200, 210, 212, 220, 240, 300, 312, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1032, 1100, 1101, 1102, 1104, 1110, 1111, 1112, 1120, 1200, 1210, 1212, 1220, 1320, 2000, 2010, 2012, 2020, 2100, 2110, 2112

Offset: 1

Jaroslav Krizek, Mar 25 2011

			Number 30 is in sequence because 30 is divisible by the product of factorials 3!*0! = 6.

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

Cf. A061602, A066459, A093325.

Cf. A066459, A000142, A197181.

import Data.List (elemIndices)
a188264 n = a188264_list !! (n-1)
a188264_list =
   map (+ 1) $ elemIndices 0 $ zipWith mod [1..] $ map a066459 [1..]
-- Reinhard Zumkeller, Oct 11 2011

Select[Range[2200],Divisible[#,Times@@(IntegerDigits[#]!)]&] (* Harvey P. Dale, May 24 2017 *)

A247227 Numbers that divide the sum of the factorials of their digits in base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 56, 71, 93, 145, 219, 758, 768, 7584, 7684, 9696, 10081, 21993, 40585

Offset: 1

Jaroslav Krizek, Dec 25 2014

Numbers n such that n divides A061602(n).
Finite sequence with 23 terms.
Subsequence of numbers n such that A061602(n) >= n. The largest such number is 1999999.
Sequence of values A061602(a(n)) / a(n): 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 19099, 15, 71, 3902, 1, 1657, 60, 60, 6, 6, 75, 4, 33, 1.
Supersequence of A014080 (whose terms are the numbers n such that A061602(n) / n = 1).

			19 is in the sequence because 19 divides 1! + 9! = 1 + 362880 = 362881; 362881 / 19 = 19099.

Cf. A014080, A061602, A093325, A197181.

[n: n in [1..2000000] | &+[ Factorial(d): d in Intseq(n)] mod n eq 0]

Select[Range[50000], Mod[Plus @@ Factorial[IntegerDigits[#]], #] == 0 &] (* Michael De Vlieger, Dec 26 2014 *)

for(k=1,10^5,d=digits(k);s=sum(i=1,#d,d[i]!);if(!(s%k),print1(k,", "))) \\ Derek Orr, Dec 30 2014

A261556 Numbers that divide the sum of the product of the factorials of their digits and the sum of the factorials of their digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 17, 54, 86, 573, 768, 999, 6143, 94584, 159287, 27167549, 40548073, 72382636, 131092614, 340720926, 1161216721, 2955383683, 3892089702, 5304046976, 6554754648, 72338498624, 279445396448, 331043595868, 466026097373, 962499474063, 3082891291712

Offset: 1

Paolo Omodei-Zorini, Aug 24 2015

			54 is in the list because 5! = 120, 4! = 24,  120*24=2880, 120+24=144, 2880+144=3024, 3024/54=56.

Cf. A197181, A247227.

fQ[n_] := Block[{d = IntegerDigits[n]!}, Mod[Times @@ d + Total@ d, n] == 0]; Select[Range@ 1000000, fQ] (* Michael De Vlieger, Aug 26 2015 *)

isok(n) = my(d = digits(n)); ((sum(k=1,#d, d[k]!)+prod(k=1,#d, d[k]!)) % n) == 0; \\ Michel Marcus, Aug 25 2015

a(24)-a(25) from Jon E. Schoenfield, Aug 24 2015
a(26)-a(30) from Giovanni Resta, Aug 26 2015
a(31)-a(34) from Chai Wah Wu, May 04 2019
a(35) from Giovanni Resta, Aug 19 2019

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A188264 Numbers m that are divisible by the product of the factorials of their digits in base 10.

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A247227 Numbers that divide the sum of the factorials of their digits in base 10.

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A261556 Numbers that divide the sum of the product of the factorials of their digits and the sum of the factorials of their digits.

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