%I
%S 4,8,9,27,32,36,49,128,841,5184
%N Perfect powers equal to the sum of three factorial numbers.
%C a(11), if it exists, is larger than 10^100.
%C a(11), if it exists, is larger than 1024!.  _Filip Zaludek_, Sep 08 2018
%H Giovanni Resta, <a href="/A114377/a114377.txt">Decompositions for a(1)a(10)</a>
%e a(1) = 4 because 4 = 1! + 1! + 2!;
%e a(2) = 8 because 8 = 1! + 1! + 3!;
%e a(3) = 9 because 9 = 1! + 2! + 3!.
%Y Cf. A082875, A227644A227651,
%K nonn
%O 1,1
%A _Giovanni Teofilatto_, Feb 10 2006
%E Offset corrected by _Arkadiusz Wesolowski_, Mar 06 2013
%E Example corrected by and a(9)a(10) from _Giovanni Resta_, Jul 19 2013
