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∑MathAdvanced

Möbius Function and Inversion

The Möbius function μ(n) is 0 if n has a squared prime factor, otherwise it is (-1)^k where k is the number of distinct prime factors.

#mobius function#mobius inversion#dirichlet convolution+12

∑MathIntermediate

Linear Sieve

The linear sieve builds all primes up to n in O(n) time by ensuring each composite is marked exactly once by its smallest prime factor (SPF).

Filtering by:

#totient

#smallest prime factor

#spf

+12

∑MathIntermediate

Prime Factorization

Prime factorization expresses any integer greater than 1 as a product of primes raised to powers, uniquely up to ordering.

#prime factorization#trial division#spf sieve+12