A162681 Numbers k such that k^2 is a sum of three factorials.

2, 3, 6, 7, 29, 72

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 10 2009

Keywords

• nonn

Comments

The next term after 72 is larger than 10^40 (if it exists). - R. J. Mathar, Jul 16 2009

Examples

			2^2 = 1! + 1! + 2!;
3^2 = 1! + 2! + 3!;
6^2 = 3! + 3! + 4!;
7^2 = 1! + 4! + 4!;
29^2 = 1! + 5! + 6!;
72^2 = 4! + 5! + 7!.
		

Crossrefs

Cf. A065433, A082875.

Programs

Maple

s := 10^40 ; sqr := s^2 : for a from 1 do if a! > sqr then break; fi; for b from a do if a!+b! > sqr then break; fi; for c from b do if a!+b!+c! > sqr then break; fi; if issqr(a!+b!+c!) then print( sqrt(a!+b!+c!)); fi; od: od: od: # R. J. Mathar, Jul 16 2009
w := 7: f := proc (x, y, z) options operator, arrow: sqrt(factorial(x)+factorial(y)+factorial(z)) end proc: A := {}: for x to w do for y to w do for z to w do if type(f(x, y, z), integer) = true then A := `union`(A, {f(x, y, z)}) else end if end do end do end do: A; # Emeric Deutsch, Aug 03 2009

Mathematica

$MaxExtraPrecision=Infinity; lst={};Do[Do[Do[x=(a!+b!+c!)^(1/2);If[x==IntegerPart[x], AppendTo[lst,x]],{c,b,2*4!}],{b,a,2*4!}],{a,2*4!}];Union[lst]

Extensions

Definition rephrased by R. J. Mathar, Jul 16 2009