  Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest
parts partition function spt(n). These congruences are reminiscent of
Ramanujan's partition congruences modulo powers of 5, 7 and 11. Recently, Ono
proved explicit Ramanujan-type congruences for spt(n) modulo p for all primes
p>3 which were conjectured earlier by the author. We extend Ono's method to
handle the powers of 5, 7 and 13 congruences. We need the theory of weak Maass
forms as well as certain classical modular equations for the Dedekind
eta-function.
