# Integer totient

`integer-totient` · version 1.0.0 · Numbers & math · free, no key needed

Compute Euler's totient function: the count of integers in [1, value] coprime to value.

**Use when you need to: integer totient · euler's totient function · euler phi function.**

## Supported

- integer totient
- euler's totient function
- euler phi function
- count coprime integers

## Not supported

- totient of 0 or negative integers
- carmichael function
- totient summatory function

## Behavior

- value is a canonical positive integer string from 1 to 1000000000000 (10^12) inclusive.
- 0 and negative values are rejected: the totient is only defined here for positive integers.
- value 1 returns 1 by convention (the empty product / one coprime residue).
- Computed exactly from the prime factorization as value * product over distinct primes p dividing value of (1 - 1/p), using integer arithmetic only (no floating point).
- Derivation uses exact trial division up to sqrt(value), bounded by the 10^12 input cap for predictable running time.

## Input

- `value` (string, required): max length 13; pattern `^[1-9][0-9]*$`

## Output

- `value` (string, required)

## Limits

- max value: 1000000000000
- max digits: 13

## Example

Request input:

```json
{
  "value": "36"
}
```

Response:

```json
{
  "result": {
    "value": "12"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "integer-totient",
  "version": "1.0.0",
  "input": {
    "value": "36"
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/integer-totient/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"value":"36"}'
```

The machine-readable contract is at [/v1/tools/integer-totient/versions/1.0.0](/v1/tools/integer-totient/versions/1.0.0).

### CLI

```sh
node cli.mjs run integer-totient 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Array integer GCD](/tools/array-integer-gcd): Compute the non-negative greatest common divisor of an array of canonical integer strings.
- [Array integer LCM](/tools/array-integer-lcm): Compute the non-negative least common multiple of an array of canonical integer strings.
- [Array integer min max](/tools/array-integer-min-max): Return the numeric minimum and maximum of canonical integer strings.
- [Array integer mode](/tools/array-integer-mode): Return the most frequent canonical integers, listing every mode in first-seen order.
- [Array integer ranks](/tools/array-integer-ranks): Assign competition (1224) ranks to canonical integers; ties share the minimum rank.
- [Integer add](/tools/integer-add): Add two canonical signed integer strings and return their canonical sum.