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- from hypothesis import given
- from hypothesis import strategies as st
- from sympy import divisors
- from sympy.functions.combinatorial.numbers import divisor_sigma, totient
- from sympy.ntheory.primetest import is_square
- @given(n=st.integers(1, 10**10))
- def test_tau_hypothesis(n):
- div = divisors(n)
- tau_n = len(div)
- assert is_square(n) == (tau_n % 2 == 1)
- sigmas = [divisor_sigma(i) for i in div]
- totients = [totient(n // i) for i in div]
- mul = [a * b for a, b in zip(sigmas, totients)]
- assert n * tau_n == sum(mul)
- @given(n=st.integers(1, 10**10))
- def test_totient_hypothesis(n):
- assert totient(n) <= n
- div = divisors(n)
- totients = [totient(i) for i in div]
- assert n == sum(totients)
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