On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138472We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained results enable us to understand better the properties of these numbers and their asymptotic behavior. On the basis of these identities a simple proof of the Prime Number Theorem is represented.11 pages, revised versionNumber Theory11N05, 11A41On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theoremtext