For each positive integer k, let d(k) be the number of positive divisors of k and σ(k) be the sum of positive divisors of k. Let N be the set of all positive integers. Find all functions f:N→N such that \begin{align*}
f(d(n+1)) &= d(f(n)+1) \text{and} \\
f(\sigma(n+1)) &= \sigma(f(n)+1)
\end{align*}
for all positive integers n. number theoryNumber theoretic functionsArithmetic Functionsfunctional equation