Question 82
a) There exists a unique sequence of positive integers $a_1, a_2, a_3, \dots$ such that
$$
n = \sum_{d|n} a_d, \quad \text{for all } n \in \mathbb{N}^*.
$$
b) There exists a unique sequence of positive integers $b_1, b_2, b_3, \dots$ such that
$$
n = \prod_{d|n} b_d, \quad \text{for all } n \in \mathbb{N}^*.
$$
$$
n = \sum_{d|n} a_d, \quad \text{for all } n \in \mathbb{N}^*.
$$
b) There exists a unique sequence of positive integers $b_1, b_2, b_3, \dots$ such that
$$
n = \prod_{d|n} b_d, \quad \text{for all } n \in \mathbb{N}^*.
$$