number of distinct prime factors of a number

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There is a function to list the prime divisors or prime factors.

It is called prime_divisors, and aliased as prime_factors.

The len function can then give the number of prime factors.

sage: a = 234

sage: prime_divisors(a)
[2, 3, 13]
sage: len(prime_divisors(a))
3

sage: prime_factors(a)
[2, 3, 13]
sage: len(prime_factors(a))
3

The function prime_divisors and its alias prime_factors also exist as methods of integers.

sage: a.prime_divisors()
[2, 3, 13]
sage: len(a.prime_divisors())
3

sage: a.prime_factors()
[2, 3, 13]
sage: len(a.prime_factors())
3