Abstract. We evaluate the odd-partition function p2(n) modulo 4 by elementary methods and analyze the asymptotic distribution of p2(n) modulo 4. We use the theory of modular forms to obtain necessary and sufficient conditions for the order at 2 of p2(n) to equal any given value between 0 and 4 inclusive.
Mehelich, Chris, "The order at 2 of the odd-partition function" (2002). Mathematical Sciences Technical Reports (MSTR). 88.