Let M(n)=(N3(n)/48), where N3(n) denotes the number of ways in which n can be written as sum of three squares. We study the congruence properties of some partition functions in relation to M(16n + 14).

Let G(n) denote the number of partitions of n into distinct parts which are of the form 2m, 3m, 5m, 6m-3, 8m-3, 9m-3 or 11m-3 with parts of the form 2m, 3m, 6m-3, or 11m-3 being even in number minus the number of them with ...