ALEKSANDAR IVIG ON THE ITERATES OF THE ENUMERATING FUNCTION OF FINITE ABELIAN GROUPS

Let a(n) denote the number of non-isomorphic Abelian (commutative) groups with n elements. It is well known that (see [5]) a(n) is a multiplicative function of n (a(mn)=a(m)a(n) for coprime m and n) such that a(pk)=P(k) for every prime p and integer k>1 (here and later p, pi, p.2, . . . denote primes), where P(k) is the number of unrestricted parititons of k . Hence P(1)=1, P(2)=2, P(3)=3, P(4)=5, and as k-->oo