Ω ( n ) = α 1 + α 2 + . . . . . + α i + . . . . . . + α r − 1 + α r {\displaystyle \Omega \left(n\right)=\alpha _{1}+\alpha _{2}+.....+\alpha _{i}+......+\alpha _{r-1}+\alpha _{r}} si
n = ( p 1 ) α 1 × ( p 2 ) α 2 × . . . . . ( p i ) α i × . . . . . × ( p r − 1 ) α r − 1 × ( p r ) α r {\displaystyle 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}}}
λ ( n ) = ( − 1 ) ( α 1 + α 2 + . . . . . + α i + . . . . . . + α r − 1 + α r ) {\displaystyle \lambda \left(n\right)=\left(-1\right)^{\left(\alpha _{1}+\alpha _{2}+.....+\alpha _{i}+......+\alpha _{r-1}+\alpha _{r}\right)}} si
λ ( n ) = ( − 1 ) ( ∑ j = 1 n ( ∑ i = 1 n ( [ [ n i j ] ( n i j ) ] × ( 1 − [ [ ( i ! ) 2 i 3 ] ( i ! ) 2 i 3 ] ) ) ) ) {\displaystyle \lambda \left(n\right)=\left(-1\right)^{\left(\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)\right)}}
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Liouville selon Laine Jean Lhermite Junior
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![{\displaystyle \lambda \left(n\right)=\left(-1\right)^{\left(\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)\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/15ebb460496e5b870bf8ba9b0928105acb3fb6e5)
