Divisor Sigma Function

Calculus Level 5

If

\[S=\displaystyle \sum_{p} \displaystyle \sum_{n=2}^{\infty} \dfrac{\tau (n)-1}{p^n}\]

where \(p\in\mathbb{N}\) is greater than 1 and is NOT a perfect power.

Find \(\lceil 10000S \rceil\)

Notes:

  • \(\tau (x)\) is the divisor sigma function. This represents the number of factors of a number including 1 and itself. For example, \(\tau(6)=\sigma_0(6)=4\).

  • \( \lceil \cdot \rceil \) denotes the ceiling function.

×

Problem Loading...

Note Loading...

Set Loading...