A059589 Sums of factorials of distinct integers.

1, 2, 3, 4, 6, 7, 8, 9, 10, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 720, 721, 722, 723, 724, 726, 727, 728, 729, 730, 744, 745, 746, 747, 748, 750, 751, 752, 753

Offset: 1

Author

Henry Bottomley, Jan 24 2001

Keywords

• nonn

Comments

0! and 1! are treated as distinct.

From Bernard Schott, Apr 13 2017: (Start)

Factorial numbers (A000142) are included in this sequence.

Only one factorial (2!) is the sum of distinct factorials in more than one way: 2! = 0! + 1!.

(End)

Sequence contains the same nonzero terms as A059590, and in addition also each term immediately after each maximal run of consecutive terms in A059590. For example, because A059590 contains numbers 30, 31, 32, 33, this sequence contains the same four terms, and also 34 which follows them but is not included in A059590. - Antti Karttunen, Apr 15 2017

Examples

			128 is in the sequence since 5! + 3! + 2! = 128.
2 = 0! + 1!.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000142, A059590 (subsequences).

Cf. A014597, A025494, A051760, A051761.

Programs

Mathematica

Rest@Union[Plus @@@ (Subsets@Range[0, 6]!)] (* Ivan Neretin, Jun 05 2016 *)