# Is it Number Theory or Combinatorics ?

For $$k≥1$$, let $$a_{k}$$ be the greatest divisor of $$k$$ which is not a multiple of $$3$$.

Set $$S_{0}=0$$ and $$S_{k}=a_{1}+a_{2}+...+a_{k}$$ for $$k≥1$$.

Find the number of integers $$k$$ with $$0≤k<3^{15}$$ such that $$S_{k}$$ is divisible by $$3$$.

Note A generalization of this problem was once proposed for IMO.

Try other interesting combinatorics in my set Hard

×