Question

Let f be the unique function defined on the positive integers. What is f(2023), where (f(n) = sum_d|n d) and the sum is taken over all positive divisors of n?

a) 2019
b) 2022
c) 2023
d) 4046

Answer 1

To calculate f(2023), the sum of all positive divisors of 2023 must be found. Factoring 2023 gives us 7 and 17 as prime factors, leading to the divisors 1, 7, 17, 119, 289, and 2023.

Step-by-step explanation:

The student is asking to find the sum of all positive divisors of the number 2023, which is represented by the function f(n) where n is a positive integer. To find f(2023), we must find all the positive divisors of 2023 and add them up. First, we factorize 2023. The prime factors of 2023 are 7 and 17 since 2023 = 7 × 17 × 17 (since 2023 = 119 x 17 and 119 = 7 x 17). Therefore, the positive divisors of 2023 are 1, 7, 17, 119, 289, and 2023. Adding them together, we get 1 + 7 + 17 + 119 + 289 + 2023 = 2456.

However, none of the options provided in the question match this result, which indicates there might be an error in the question or the options given. Typically, such a function is known as the divisor function, usually represented by σ(n), which is different from what is represented in the question as f(n).