Representation of Integers: A nonclassical point of view

BOUDAOUD ABDELMADJID BELLAOUAR DJAMEL

In the Introduction, this paper defines functions ω and Ω which give the number of distinct prime divisors and the total number of prime factors of a number. We define these and calculate some examples.

def Ω (n : ℕ) : ℕ

Equations

• Ω n = n.primeFactorsList.length

def ω (n : ℕ) : ℕ

Equations

• ω n = (Finset.filter (fun (p : Fin n.succ) => Nat.Prime ↑p ∧ padicValNat (↑p) n > 0) Finset.univ).card