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Numbers that divide the sum of the factorials of their digits in base 10.
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%I #19 Sep 08 2022 08:46:09

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

%T 21993,40585

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

%C Numbers n such that n divides A061602(n).

%C Finite sequence with 23 terms.

%C Subsequence of numbers n such that A061602(n) >= n. The largest such number is 1999999.

%C 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.

%C Supersequence of A014080 (whose terms are the numbers n such that A061602(n) / n = 1).

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

%t Select[Range[50000], Mod[Plus @@ Factorial[IntegerDigits[#]], #] == 0 &] (* _Michael De Vlieger_, Dec 26 2014 *)

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

%o (PARI) 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

%Y Cf. A014080, A061602, A093325, A197181.

%K nonn,base,fini,full

%O 1,2

%A _Jaroslav Krizek_, Dec 25 2014