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Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallestparts partition function spt(n). These congruences are reminiscent ofRamanujan's partition congruences modulo powers of 5, 7 and 11. Recently, Onoproved explicit Ramanujan-type congruences for spt(n) modulo p for all primesp>3 which were conjectured earlier by the author. We extend Ono's method tohandle the powers of 5, 7 and 13 congruences. We need the theory of weak Maassforms as well as certain classical modular equations for the Dedekindeta-function.

Congruences for Andrews’ spt-function modulo powers of $5$, $7$ and $13$