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Problem 3003. Mobius function

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From wikipedia:
For any positive integer n, define μ(n) as the sum of the primitive n-th roots of unity. It has values in {−1, 0, 1} depending on the factorization of n into prime factors:
  • μ(n) = 1 if n is a square-free positive integer with an even number of prime factors.
  • μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors.
  • μ(n) = 0 if n has a squared prime factor.
Return numbers from the Mobius function sequence corresponding to the supplied indices. For example, if n = 3:7, your function should return [-1, 0, -1, 1, -1].
Hint: solving Problem 3001 and Problem 3002 will provide much of the code needed for this problem. You'll need to add prime numbers to the sphenic number set (resulting from Problem 3001).
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47.76% Correct | 52.24% Incorrect
Last Solution submitted on May 05, 2025

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