Fonksyon omega ki konte kantite nonm premye ki diferan ki divize yon nonm n

Fonksyon $\omega$ [modifye | modifye kòd]

Si dekonpozisyon kanonik n se :

$n=\left(p_{1}\right)^{{\alpha }_{1}}\times \left(p_{2}\right)^{{\alpha }_{2}}\times .....\left(p_{i}\right)^{{\alpha }_{i}}\times .....\times \left(p_{r-1}\right)^{{\alpha }_{r-1}}\times \left(p_{r}\right)^{{\alpha }_{r}}$

avèk $p_{i}$ diferan youn ak lòt e $\alpha _{i}$ pi gran ou egal ak 1 , nou genyen :

$\omega \left(n\right)=\sum _{p|n}1=r$

Ekspresyon fonksyon $\omega$ selon Lainé Jean Lhermite Lainé Junior[modifye | modifye kòd]

$\omega \left(n\right)=\sum _{i=1}^{n}{\left({{\left[{\frac {\left[{\frac {n}{i}}\right]}{\left({\frac {n}{i}}\right)}}\right]}\times \left(1-\left[{\frac {\left[{\frac {\left(i!\right)^{2}}{i^{3}}}\right]}{\frac {\left(i!\right)^{2}}{i^{3}}}}\right]\right)}\right)}$