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

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

Author

Jaroslav Krizek, Dec 25 2014

Keywords

• nonn
• base
• fini
• full

Comments

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).

Examples

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

Crossrefs

Cf. A014080, A061602, A093325, A197181.

Programs

Magma

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

Mathematica

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

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