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On the density of a particular subset of integers
Given a positive integer $n$ in the standard form
$$n=\prod_k p_k^{\alpha_k}$$
and the arithmetic function (investigated by Erdős in this paper)
$$A(n)=\sum_k \alpha_k p_k$$
let's define the subset $E$...
- 1,008
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Given $\,m=\prod_k {p_k}^{\alpha_k}\,$ and the function $\,g(m)=\sum_k \alpha_k(p_k-1)^2$, find all solutions of the equation $\,g(2n)=n$
Let's consider the unique decomposition of a natural number $\,m\,$ into its prime factors:
$$\prod_k {p_k}^{\alpha_k}$$
Then, let's define the following arithmetic function (completely additive) $\,g:...
- 1,008