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Math Help - Prove sum of lamda d

  1. #1
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    Prove sum of lamda d

    Prove that  \sum_{d|n}\lambda(d)= \left\{\begin{array}{ll}1,&\mbox{  if   } n=m^2 \mbox{  for some  m}\\0,&\mbox{   otherwise   } \end{array}\right.

    where \lambda(n)= (-1)^{\Omega(n)} and \Omega(n) is the number of prime divisors of n counting multiplicity.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Hint : express the sum as a product taken over the prime powers which divide n. (Use the fact that Liouville's function is multiplicative.)
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