Definition:Divisor Count Function/Also known as

Divisor Count Function: Also known as

Some sources refer to this as the divisor function and denote it $\map d n$.

However, as this function is an instance of a more general definition of the divisor function, on $\mathsf{Pr} \infty \mathsf{fWiki}$ the more precise name divisor count function is preferred.

It is also often referred to as the $\tau$ (tau) function, but there are a number of functions with such a name.

Some sources use $\nu$, but again, that also has multiple uses.

Hence the unwieldy, but practical, divisor count function, which is non-standard.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): Glossary
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): divisor function
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): sigma function or $\sigma$ function: 2.
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): Glossary
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): divisor function
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): divisor function