MathDB

3

Part of 2017 Bosnia and Herzegovina EGMO TST

Problems(1)

Bosnia and Herzegovina EGMO TST 2017 Problem 3

Source: Bosnia and Herzegovina EGMO Team Selection Test 2017

9/19/2018
For positive integer nn we define f(n)f(n) as sum of all of its positive integer divisors (including 11 and nn). Find all positive integers cc such that there exists strictly increasing infinite sequence of positive integers n1,n2,n3,...n_1, n_2,n_3,... such that for all i∈Ni \in \mathbb{N} holds f(ni)−ni=cf(n_i)-n_i=c
Sequencenumber theoryDivisors