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:

{
  "value": "36"
}

Response:

{
  "result": {
    "value": "12"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

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

HTTP (no key)

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.

CLI

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

Get the client at /clients/cli/.

Related tools

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