Concepts3
βMathAdvanced
MΓΆbius Function and Inversion
The MΓΆbius function ΞΌ(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
βMathIntermediate
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).
#linear sieve#smallest prime factor#spf+12
βMathIntermediate
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