A244090 Numbers n such that n is a factorion (A014080, equal to the sum of the factorials of its digits), in at least one base b.

1, 2, 7, 25, 26, 48, 49, 121, 122, 144, 145, 240, 721, 722, 726, 1440, 1441, 1442, 5041, 5042, 5162, 5760

Offset: 1

Author

Anthony Sand, Jun 20 2014

Keywords

• nonn
• base
• more

Comments

The bases in which n = func(n) are 2, 2, 4, 6, 6, 11, 5, 24, 24, 28, 10, 47, 120, 120, 240, 239, 15, 15, 720, 720, 27, 822. Note multiple bases for some n, e.g. 25 = 4! + 1! in base 6 and 25 = 1! + 4! in base 21; 721 = 6! + 1! in base 120 and 721 = 1! + 6! in base 715.

Examples

			1 = 1! = 1 (base>=2).
2 = 1! + 0! = 1 + 1 = 10 (b=2).
7 = 1! + 3! = 1 + 6 = 13 (b=4).
25 = 4! + 1! = 24 + 1 = 41 (b=6).
26 = 4! + 2! = 24 + 2 = 42 (b=6).
48 = 4! + 4! = 24 + 24 = 44 (b=11).
49 = 1! + 4! + 4! = 1 + 24 + 24 = 144 (b=5).
121 = 5! + 1! = 120 + 1 = 51 (b=24).
122 = 5! + 2! = 120 + 2 = 52 (b=24).
144 = 5! + 4! = 120 + 24 = 54 (b=28).
145 = 1! + 4! + 5! = 1 + 24 + 120 (b=10).
240 = 5! + 5! = 120 + 120 = 55 (b=47).
		

Links

• Wikipedia, Factorion

Crossrefs

Cf. A193163, A014080.

Programs

PARI

isok(n) = {if (n==1, return (1)); for (b=2, n, d = digits(n, b); if (sum(i=1, #d, d[i]!) == n, return (1));); return (0);} \\ Michel Marcus, Jun 21 2014

Formula

s = 0; for digit(i=1..j) of n in base b, s = s + digit(i)!.