MathDB

4

Part of 2023 CIIM

Problems(1)

Find the limsup!

Source: CIIM 2023 - Problem 4

9/19/2023
For a positive integer nn, σ(n)\sigma(n) denotes the sum of the positive divisors of nn. Determine lim sup⁡n→∞σ(n2023)(σ(n))2023\limsup\limits_{n\rightarrow \infty} \frac{\sigma(n^{2023})}{(\sigma(n))^{2023}}
Note: Given a sequence (ana_n) of real numbers, we say that lim sup⁡n→∞an=+∞\limsup\limits_{n\rightarrow \infty} a_n = +\infty if (ana_n) is not upper bounded, and, otherwise, lim sup⁡n→∞an\limsup\limits_{n\rightarrow \infty} a_n is the smallest constant CC such that, for every real K>CK > C, there is a positive integer NN with an<Ka_n < K for every n>Nn > N.
limit superiorlimitsum of divisorsreal analysis