PSQL - query to determin if a defined interval is matched

I have a PSQL DB with two tables, "months" and "obligations"

"obligations.start_month" is foreign key´d to "months.id"

months
======
id  alias
--  -----
1   01.2021
2   02.2021
3   03.2021
4   04.2021
5   05.2021
6   06.2021


obligations
===========
id  alias   start_month interval_months
--  -----   ----------- ---------------
1   one     1           1
2   two     1           2
3   three   3           3

I am looking for the SQL question to the answer which obligation falls within the asked for month.

This is my best attempt yet, n being replaceable:

select * 
from obligations
where
start_month <= 3
and start_month + (n*interval_months) = 3

Most likely the last line of my query anyways needs to be rewritten, but I am lacking ideas of how. I want to have all the rows, that are either in the start_month or fit into the interval. If asking for month 3, it should return obligation 1(occuring every month) and 2(starting in month 1 + every other month , so in 3, 5, 7, and so on) and obligation 3(starting in month 3). The data is not explicitely stating that, so i need to calculate , based on the start month + n-times the interval and looking if it matches. Basically, for the scenario sketched above, it should return like that:

month   obligations_matching
----    --------------------
1       one
        two

2       one

3       one
        two
        three

4       one

5       one
        two

6       one
        three

I am fiddling with things like "generate_series" to allow multiple calculation operations for the different interval scenarios but can not seem to wrap my head around it well enough. I can find the interval MANUALLY by KNOWING the multiplier, but can not automate this process.

Any input how to handle the variable multiplicator(1*interval_months)?

Kind regards Martin

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