# Definition:Prime-Counting Function/Examples

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## Definition

The values of the prime-counting ($\pi$) function for the first few integers are as follows:

$n$ $\map \pi n$ $1$ $0$ $2$ $1$ $3$ $2$ $4$ $2$ $5$ $3$ $6$ $3$ $7$ $4$ $8$ $4$

This sequence is A000720 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

### 16

The value of the prime-counting ($\pi$) function for $16$ is determined as follows.

The prime numbers less than $16$ are:

- $2, 3, 5, 7, 11, 13$

Hence:

- $\map \pi {16} = 6$

## Sources

- 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Example $2.1.1$