In this paper, we prove several new infinite families of Ramanujan–like congruences satisfied by the coefficients of the generating function Ut(a,q) which is an extension of MacMahon’s generalized sum-of-divisors function. As a by-product, we also show that, for all n≥0, B¯3(15n+7)≡0(mod5) where B¯3(n) is the number of almost 3-regular overpartitions of n.
Sellers, J.a., Tauraso, R. (2025). Arithmetic properties of MacMahon-type sums of divisors. RAMANUJAN JOURNAL, 67(2) [10.1007/s11139-025-01097-4].
Arithmetic properties of MacMahon-type sums of divisors
Roberto Tauraso
2025-01-01
Abstract
In this paper, we prove several new infinite families of Ramanujan–like congruences satisfied by the coefficients of the generating function Ut(a,q) which is an extension of MacMahon’s generalized sum-of-divisors function. As a by-product, we also show that, for all n≥0, B¯3(15n+7)≡0(mod5) where B¯3(n) is the number of almost 3-regular overpartitions of n.File in questo prodotto:
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