Is there a name for when two numbers have the same sums of divisors?

Question

If $a,b$ are integers and $\sigma$ is the sum of divisors function and $\sigma (a) = \sigma (b)$ is there a name for this? For instance $\sigma (14) = \sigma (15) = 24$

Answer 1

Amicable numbers are also quite similar to what you are asking for, perhaps more similar than friendly numbers. You may also want to look at the aliquot sum (denoted as $s(n)=\sigma(n)-n$).

Edit: One concept I have noticed that may aid the OP is the following:

If $\text{gcd}(n,k)=1$, then $\sigma(nk) = \sigma(n)\sigma(k)$.

So, if you know the prime factorisation of any number $s$, $\sigma(s)=\sigma(s_{p_1})\sigma(s_{p_2})\cdots\sigma(s_{p_n})$ (where $s_{p_n}$ denotes the $n$th prime factor of $s$.)