A115647 Triangular numbers that are sums of distinct factorials.

1, 3, 6, 120, 153, 5886, 40470, 41041, 40279800

Offset: 1

Author

Giovanni Resta, Jan 27 2006

Keywords

• nonn

Comments

Factorials 0! and 1! are not considered distinct.

A115944(a(n)) > 0; subsequence of A059590. - Reinhard Zumkeller, Feb 02 2006

If there are any terms beyond 40279800 they must be larger than 48!. - Jon E. Schoenfield, Aug 04 2006

Examples

			1 = T(1) = 1!.
3 = T(2) = 2!+1!.
6 = T(3) = 3!.
120 = T(15) = 5!.
153 = T(17) = 5!+4!+3!+2!+1!.
5886 = T(108) = 7!+6!+5!+3!.
40470 = T(284) = 8!+5!+4!+3!.
41041 = T(286) = 8!+6!+1!.
40279800 = T(8975) = 11!+9!+5!.
		

Links

• Shyam Sunder Gupta, Triangular Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 83-125. See also Fascinating Factorials, Ch. 16, 411-442.

Crossrefs

Cf. A025494.

Programs

Mathematica

triQ[n_] := IntegerQ@Sqrt[8n+1]; fac=Reverse@Range[21]!; lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 21]); If[triQ[n], AppendTo[lst, n]; Print[{n, k}]], {k, 2^21-1}]; Union@lst