ARTICLE | doi:10.20944/preprints202104.0297.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: generalized hyperharmonic numbers, classical Euler sums, binomial coefficients, combinatorial approach, partial fraction approach
Online: 12 April 2021 (12:43:36 CEST)
In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.
ARTICLE | doi:10.20944/preprints202112.0423.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sums over primes; generalized alternating hyperharmonic numbers; asymptotic formula; numbers with $k$-prime factors
Online: 27 December 2021 (11:10:43 CET)
In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers of types I, II and III. Analogous results for numbers with $k$-prime factors will also be considered.