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

1,2

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A000142, A059590 (subsequences).

Cf. A014597, A025494, A051760, A051761.

Sequence in context: A376595 A343732 A039168 * A153287 A244219 A039258

Adjacent sequences: A059586 A059587 A059588 * A059590 A059591 A059592

Keyword

nonn

Author

Henry Bottomley, Jan 24 2001

Status

approved