Fonksyon Omega ki konte kantite faktè premye ki rantre nan dekonpozisyon yon nonm antye n

Fonksyon $\Omega$ [modifye | modifye kòd]

$\Omega \left(n\right)=\alpha _{1}+\alpha _{2}+.....+\alpha _{i}+......+\alpha _{r-1}+\alpha _{r}$
si nou gen dekonpozisyon kanonik sa pou n :

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

Ekspresyon Fonksyon $\Omega$ selon Lainé Jean Lhermite Junior[modifye | modifye kòd]

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