Arithmetic functions

Concepts

• Multiplicative arithmetic function 10 exercisesAn arithmetic function f is multiplicative if f(1)=1 and f(mn)=f(m)f(n) whenever gcd(m,n)=1. Its behavior is determined by its va…
• Divisor functions 10 exercisesThe divisor functions σ_k(n) and τ(n) give, respectively, the sum of the k -th powers and the number of positive divisors of an i…
• Perfect number 10 exercisesA perfect number is a positive integer n equal to the sum of its proper divisors, those smaller than n; with the divisor-sum func…
• Möbius function 10 exercisesThe Möbius function μ(n) is an arithmetic function: it equals 1 if n=1, (-1)^k if n is a product of k distinct primes, and 0 if n…
• Möbius inversion formula 10 exercisesFormula that recovers an arithmetic function f from its sum over divisors, using the Möbius function μ.