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# Pólya's conjecture

Pólya's conjecture states that for any ${\displaystyle n>1}$, at least half the numbers up to ${\displaystyle n}$ have an odd number of prime factors, which are counted with multiplicity. Put another way, defining Liouville's summatory function ${\displaystyle L(n)=\sum _{i=1}^{n}(-1)^{\Omega (i)}}$, then ${\displaystyle L(n)<1}$ holds for all ${\displaystyle n>1}$, where ${\displaystyle \Omega (i)}$ is the number of prime factors function. (See A002819 for ${\displaystyle L(n)}$).