## What is this algorithm used for?

I came across this Algorithm and was wondering what exactly it is, how it's called and what to use it on...

The code (`Python`

) is this:

def unknown(n): n = abs(n) a = 0 t = 2 while t <= n: if n % t == 0: a += 1 n /= t else: t += 1 return a

here some results:

0 -> 0 1 -> 0 2 -> 1 3 -> 1 4 -> 2 5 -> 1 6 -> 2 7 -> 1 8 -> 3 9 -> 2 10 -> 2 11 -> 1 12 -> 3 13 -> 1 14 -> 2 15 -> 2 16 -> 4 17 -> 1 18 -> 3 19 -> 1 20 -> 3 30 -> 3 101 -> 1

It brute-force counts the number of prime factors of `n`

, each counted according to its multiplicity.

`t`

is the current factor being tested and `n % t == 0`

only if `n`

is an integer multiple of `t`

. If it's divisible, `n`

is divided and the division is tried again (to account for the multiplicity of that factor); otherwise, the next integer is tried, up to (the original) `n`

. Even if the division by non-primes is tried, it doesn't skew the result because all the lower primes have already been tried, so they won't ever succeed.

An obvious optimization would be to compute and memoize the primes up to the number through an efficient algorithm, and just try them.

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It's computing the number of prime factors of `n`

. Notice that any prime returns 1.

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It's the sequence

Number of prime powers (not including 1) that divide n

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The prime factors of a number n is being calculated

for example 1= 1×1 =0 since 1 is neither prime nor composite

2 = 2×1 => 1

3 = 1×3 => 1

4 = 2×2 => 2

5 = 1×5 => 1

6 = 1×2×3 => 2

7 = 1×7 => 1

8= 2×2×2 => 3

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