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Number Theory, Part 4 - Statistics
General Stats
- This quiz has been taken 3 times
- The average score is 6 of 17
Answer Stats
| Hint | Answer | % Correct |
|---|---|---|
| What is the term for: A number, n, where the sum of its divisors (including itself) equals 2n? | Perfect Number | 100%
|
| What function counts the number of positive integers relatively prime to the function's input? | Phi-function | 100%
|
| What is counted by the function d(n)? | Divisors | 67%
|
| Have we yet discovered any numbers with the property stated in the question above that are odd? (Yes or No?) | No | 67%
|
| What Greek symbol denotes the function that sums the positive factors of the function's input? | Sigma | 67%
|
| What is the term for: A function whose domain is the set of positive integers | Arithmetic function | 33%
|
| 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? | Completely multiplicaitve function | 33%
|
| There is a one-to-one correspondence between _______ primes and perfect numbers. | Mersenne | 33%
|
| _____ 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. | Mobius | 33%
|
| 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? | Mobius function | 33%
|
| 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? | Multiplicative function | 33%
|
| What is the term for: A number, n, where the sum of its divisors is greater than 2n? | Abundant | 0%
|
| What is the term for: A number, n, where the sum of its divisors equals 2n - 1? | Almost perfect | 0%
|
| 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. | Amicable | 0%
|
| What is the term for: A number, n, where the sum of its divisors is less than 2n? | Deficient | 0%
|
| What is the term for: A number, n, where the sum of its divisors equals kn? | k-perfect | 0%
|
| What is the term for: A number, n, where the product of its divisors equals n^2? | Multiplicatively perfect | 0%
|
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