1 Answers
In number theory, the Dedekind psi function is the multiplicative function on the positive integers defined by
where the product is taken over all primes p {\displaystyle p} dividing n . {\displaystyle n.} {\displaystyle \psi } , which is the empty product, has value 1.] The function was introduced by Richard Dedekind in connection with modular functions.
The value of ψ {\displaystyle \psi } for the first few integers n {\displaystyle n} is:
The function ψ {\displaystyle \psi } is greater than n {\displaystyle n} for all n {\displaystyle n} greater than 1, and is even for all n {\displaystyle n} greater than 2. If n {\displaystyle n} is a square-free number then ψ = σ {\displaystyle \psi =\sigma } , where σ {\displaystyle \sigma } is the divisor function.