Question 132
Let $f: \mathbb{Z}_{+}^{*} \rightarrow \mathbb{Z}_{+}^{*}$ be a function defined as follows: given $n$, we write $n = 2^a \cdot (2b+1)$, with $a$ and $b$ non-negative integers, and define $f(n) = a^2 + a + 1$.
Determine the least positive integer $n$ such that $f(1) + f(2) + \cdots + f(n) \ge 123456$.
Determine the least positive integer $n$ such that $f(1) + f(2) + \cdots + f(n) \ge 123456$.