Largest proper divisor of n: Difference between revisions

<syntaxhighlight lang="j"> lpd =: (1 |}.!.1 ])&.q:</syntaxhighlight>

lpd 1+>: i.100 5 20

This works by prime factorization of n, replacingremoving the largestsmallest prime factor with 1, and then taking the product of this new list of prime factors. In J terms, we work "under" factorization, in analogy to a medical operation where the patient is "under" anaethesiaanesthesia: (put patient to sleep) rearrange guts (wake patient up).

The core logic only concerns itself with a list of prime factors; it is never even aware of the original input integer, nor the final integer result. In fact, note that the final multiplication is implicit and never spelled out by the programmer; product is the inverse of factorization, and we requested to work "under" factorization, thus J's algebra knows to apply the inverse of factorization (i.e. taking the product) as the final step.