A115646 Semiprimes (A001358) that are sums of distinct factorials.

6, 9, 25, 26, 33, 121, 122, 123, 129, 145, 146, 721, 723, 745, 746, 753, 841, 842, 843, 849, 865, 866, 871, 5041, 5042, 5065, 5071, 5161, 5163, 5169, 5186, 5191, 5761, 5767, 5793, 5905, 5906, 5911, 40321, 40322, 40323, 40345, 40346, 40353, 40441

Offset: 1

Author

Giovanni Resta, Jan 27 2006

Keywords

• nonn

Comments

Factorials 0! and 1! are not considered distinct.

Examples

			721 = 6!+1! = 7*103.
		

Crossrefs

Cf. A001358, A025494, A115645, A115644, A089359.

Programs

Mathematica

semipQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; fac=Range[10]!;lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 10]); If[semipQ[n], AppendTo[lst, n]], {k, 2^10-1}]; Union[lst]