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Properties of a sequence generated by positive integers

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

Autori: V. Copil, L. Panaitopol

Editorial: BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 50 (2), p.131-137, 2007.

Rezumat:

For every positive integer $m$ let $b_m$ be the least positive
integer such that $mb_m$ is a square. We show that
$limsuplimits_{n
ightarrow infty}(b_{n+1}-b_n)=+infty$,
$liminflimits_{n
ightarrowinfty}(b_{n+1}-b_n)=-infty$ and
$sumlimits_{i=1}^nfrac{1}{b_i}=sqrt{n}frac{zeta(3/2)}{zeta(3)}+O(ln
n)$.

Cuvinte cheie: numere prime, numere libere de patrate, siruri, serii // Prime numbers, squarefree numbers, sequences, series

URL: http://rms.unibuc.ro/bulletin/pdf/50-2/Copilmod.pdf