Let $A_{n}=\{(a_1,a_2,\ldots,a_{n}): a_i\in\mathbb{Z_{>0}}|\ \ \frac{1}{a_1}+\ldots \frac{1}{a_{n}} = 1\}$.
My question. What is $|A_n|\operatorname{mod}2$, for $n=2018$? That is what is the parity of cardinality of $A_n$, for $n=2018$.
I can solve this problem for numbers of the type $n=2^i+2^k$. But in the case $n=2018$ I find it more interesting.
Also I'm interesting where such equations can arise.