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In important work on the parity of the partition function, Ono related values of the partition function to coefficients of a certain mock theta function modulo 2. In this paper, we use M\"obius inversion to give analogous results which relate several combinatorial functions via identities rather than congruences.doi:10.1090/s0002-9939-2014-12020-x fatcat:3xkkaxa2lzhjxlh3ff6chasc4y