Euler Totient by Factorization in Python

from bisect import bisect_left

# Euler Totient by Factorization in Python
#
# PURPOSE
# Euler totient counts positive integers up to n that are coprime with n.
#
# METHOD
# For each distinct prime divisor p, remove all factors p from a working value and replace
# result with result-result/p. Handle any remaining prime factor.
#
# COMPLEXITY
# O(sqrt(n)) trial-division time and O(1) space.
#
# CONTRACT
# n >= 1. phi(1)=1.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 6.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def totient(n: int) -> int:
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 1)
    result: int = n
    p: int = 2
    while p <= n // p:
        if n % p == 0:
            while n % p == 0:
                n = n // p
            result -= result // p
        p += 1
    if n > 1:
        result -= result // n
    return result

n = 9
result = totient(n)
print(result)