%I A082875
%S A082875 4,9,49,841,36,5184
%N A082875 Squares that are the sum of three factorials.
%F A082875 a1! + a2! + a3! = z^2.
%e A082875 These appear to be the only solutions. 8 and 27 appear to be the only 
               cubes
%e A082875 that are the sum of 3 factorials. Again, it appears that 2 and 3 are 
               the only
%e A082875 powers of n satisfying a1!+a2!+a3! = z^n. The complete list of solutions 
               is
%e A082875 a1 a2 a3 z^2
%e A082875 0 0 2 4
%e A082875 0 1 2 4
%e A082875 0 2 3 9
%e A082875 0 4 4 49
%e A082875 0 5 6 841
%e A082875 1 1 2 4
%e A082875 1 2 3 9
%e A082875 1 4 4 49
%e A082875 1 5 6 841
%e A082875 3 3 4 36
%e A082875 4 5 7 5184
%t A082875 d = 50; a = Union[ Flatten[ Table[a! + b! + c!, {a, 1, d}, {b, a, d}, 
               {c, b, d}]]]; l = Length[a]; Do[ If[ IntegerQ[ Sqrt[ a[[i]]]], Print[ 
               a[[i]]]], {i, 1, l}]
%o A082875 (PARI) sum3factsq(n) = { for(a1=1,n, for(a2=a1,n, for(a3=a2,n, z = a1!+a2!+a3!; 
               if(issquare(z),print1(z" ")) ) ) ) }
%Y A082875 Sequence in context: A081069 A053967 A028945 this_sequence A086541 A053965 
               A058444
%Y A082875 Adjacent sequences: A082872 A082873 A082874 this_sequence A082876 A082877 
               A082878
%K A082875 easy,nonn
%O A082875 0,1
%A A082875 Cino Hilliard (hillcino368(AT)gmail.com), May 25 2003