Number Theory, Part 4

What function counts the number of positive integers relatively prime to the function's input?

What is counted by the function d(n)?

What Greek symbol denotes the function that sums the positive factors of the function's input?

What function outputs 1 if n equals 1 or the product of an even number of distinct primes, -1 if n is the product of an odd number of distinct primes, or 0 otherwise?

_____ inversion formula allows us to, given a function F as a sum of function G evaluated over the F's input's divisors, write the function G as a weighted sum of F over G's input's divisors, with the function that appears in the weights of our sum being the answer of the question above.

What is the term for: A function whose domain is the set of positive integers

What is the term for: A function defined on the set of positive integers, such that f(mn) = f(m)*f(n) when m, n are relatively prime?

What is the term for: A function defined on the set of positive integers, such that f(mn) = f(m)*f(n) for all integers m, n?

What is the term for: A number, n, where the sum of its divisors (including itself) equals 2n?

Have we yet discovered any numbers with the property stated in the question above that are odd? (Yes or No?)

There is a one-to-one correspondence between _______ primes and perfect numbers.

What is the term for: A number, n, where the sum of its divisors is less than 2n?

What is the term for: A number, n, where the sum of its divisors is greater than 2n?

What is the term for: A number, n, where the sum of its divisors equals 2n - 1?

What is the term for: A number, n, where the sum of its divisors equals kn?

What is the term for: A number, n, where the product of its divisors equals n^2?

Two numbers, m and n, are said to be _______ if the sum of the divisors of m equals the sum of the divisors of n, AND the sum of their divisors equals m + n.