A115644 Brilliant numbers (A078972) that are sums of distinct factorials.

6, 9, 25, 121, 841, 871, 5041, 5767, 363721, 368761, 409111, 3633841, 3992431, 3992551, 4032121, 4037791, 39962281, 39962311, 39963031, 40279711, 40279801, 43585921, 43591687, 43909207, 479047801, 479365321, 479370271, 482631271

Offset: 1

Author

Giovanni Resta, Jan 27 2006

Keywords

• nonn

Examples

			39962281 = 11! + 8! + 7! + 5!+ 1! = 4861*8221.
		

Crossrefs

Cf. A078972, A025494, A115645, A115646, A089359.

Programs

Mathematica

brillQ[n_] := Block[{d = FactorInteger[n]}, Plus@@Last/@d==2 && (Last/@d=={2} || Length@IntegerDigits@((First/@d)[[1]])==Length@IntegerDigits@((First/@d)[[2]]))]; fac=Range[20]!;lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 20]); If[brillQ[n], AppendTo[lst, n]], {k, 2^20-1}]; lst