The sum of all positive integers $$N<2024$$ such that $$N$$ equals $$13$$ times the sum of its decimal digits is

Since $$N=13s$$, where $$s$$ is the digit sum of $$N$$, the bound on a three-digit digit sum gives $$1\leq s\leq27$$. Checking these possible values in the condition that the digit sum of $$13s$$ equals $$s$$ gives $$s=9,12,15$$. The corresponding numbers are $$117,156,195$$, whose sum is $$468$$.