Fear Factoring

Given a and b up to 1e12 with b-a at most 1e6, sum the divisor sums F(n) over every n in [a, b].

Medium7Number theoryMathImplementationBrute forceNo attempts yetTime limit1sMemory limit512 MB

Description

Examples6

The Slivians are afraid of factoring. It is, well, difficult.

They do not even care about the factors themselves, only about how much they sum to.

Define $F(n)$ as the sum of all factors of $n$ , so $F(6) = 12$ and $F(12) = 28$ . Given two integers $a$ and $b$ with $a \le b$ , compute

$S=\sum_{a \le n \le b} F(n)$

The first line contains two integers $a$ and $b$ separated by a space. ( $1 \le a \le b \le 10^{12}$ , $b - a \le 10^{6}$ )

Print $S$ on a single line.