Harmonic Number Expansions of the Ramanujan Type
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DOI: 10.1007/s00025-018-0920-8
Abstract: In this paper, we establish three (general) asymptotic expansions of the Ramanujan type for the harmonic numbers, and give the corresponding recurrences of the coefficient sequence or parameter sequences in these expansions. We also present… read more here.
Keywords: ramanujan type; formula; number expansions; harmonic number ... See more keywords
Families of Ramanujan-Type Congruences Modulo 4 for the Number of Divisors
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DOI: 10.3390/axioms11070342
Abstract: In this paper, we explore Ramanujan-type congruences modulo 4 for the function σ0(n), counting the positive divisors of n. We consider relations of the form σ08(αn+β)+r≡0(mod4), with (α,β)∈N2 and r∈{1,3,5,7}. In this context, some conjectures… read more here.
Keywords: number divisors; type congruences; modulo number; families ramanujan ... See more keywords