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In this paper, we investigate the arithmetic properties for the coefficients of a sixth-order mock theta function $$\beta (q)$$ β ( q ) , which arose in the modular transformation laws by McIntosh. Several interesting congruences modulo the primes 3, 5 and 7 are obtained.
In this paper, we present an unexpected Ramanujan-type congruence modulo 7 for $$c\phi _4(n)$$ c ϕ 4 ( n ) , which denotes the number of generalized Frobenius partitions of n with 4 colors. This work extends the recent work of Lin on $$c\phi _4$$ c ϕ 4 modulo 7.
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