RU-ALLRUSSIAN 1988 Problem 13

Show that there are infinitely many odd composite numbers in the sequence $1^{1}$ , $1^{1} + 2^{2}$ , $1^{1} + 2^{2} + 3^{3}$ , $1^{1} + 2^{2} + 3^{3} + 4^{4}$ , ... .