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A sequence attached to powerful numbers

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Copil, V; Panaitopol, L

Editorial: BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 50(3), p.249-258, 2007.

Rezumat:

For every powerful number $k$, let $c_k$ be the least positive
integer such that $kc_k$ is a square. We give asymptotic
estimations for several series whose terms depend on the sequence
$(c_k)_{kgeq 1}$, from which we mention $sumlimits_{kleq x}
c_k=frac{3}{pi^2}zetaleft(frac{4}{3}
ight)sqrt[3]{x^2}+O(sqrt{x}ln
x)$.

Cuvinte cheie: numere prime, numere powerful, siruri, serii // Prime numbers, squarefree numbers, powerful numbers, sequences, series

URL: http://rms.unibuc.ro/bulletin/pdf/50-3/copilmod.pdf