Tau - the number of divisors of n

Rule

Each term is: The number of the number's divisors

Known as: Tau - the number of divisors of n

The number of divisors of n.

Tau is even when n is not a perfect square, because the divisors then occur in pairs.

The first 50 terms (starting from n=1) are:

1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 6 2 6 4 4 2 8 3 4 4 6 2 8 2 6 4 4 4 9 2 4 4 8 2 8 2 6 6 4 2 10 3 6

Example

To get the value for n=16:

  • Find the number's divisors, giving 1, 2, 4, 8, 16
  • Count them, giving 5.

So the result is 5.

References

On-Line Encyclopedia of Integer Sequences