cp's OEIS Frontend

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

%I A162681 #10 Mar 01 2019 23:33:44
%S A162681 2,3,6,7,29,72
%N A162681 Numbers k such that k^2 is a sum of three factorials.
%C A162681 The next term after 72 is larger than 10^40 (if it exists). - _R. J. Mathar_, Jul 16 2009
%e A162681 2^2 = 1! + 1! + 2!;
%e A162681 3^2 = 1! + 2! + 3!;
%e A162681 6^2 = 3! + 3! + 4!;
%e A162681 7^2 = 1! + 4! + 4!;
%e A162681 29^2 = 1! + 5! + 6!;
%e A162681 72^2 = 4! + 5! + 7!.
%p A162681 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
%p A162681 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
%t A162681 $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]
%Y A162681 Cf. A065433, A082875.
%K A162681 nonn
%O A162681 1,1
%A A162681 _Vladimir Joseph Stephan Orlovsky_, Jul 10 2009
%E A162681 Definition rephrased by _R. J. Mathar_, Jul 16 2009