Proper divisors: Difference between revisions

=={{header|J}}==

The proper divisors of an integer are the [[Factors of an integer]] without the integer itself.

So, borrowing from [[Factors of an integer#J|the J implementation]] of that related task:

<lang J>factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__

properDivisors=: factors -. -.&1</lang J>

Proper divisors of numbers 1 through 10:

<lang J> (,&": ' -- ' ,&": properDivisors)&>1+i.10

1 -- 1

2 -- 1

3 -- 1

4 -- 1 2

5 -- 1

6 -- 1 2 3

7 -- 1

8 -- 1 2 4

9 -- 1 3

10 -- 1 2 5</lang>

Number(s) not exceeding 20000 with largest number of proper divisors (and the count of those divisors):

<lang J> (, #@properDivisors)&> 1+I.(= >./) #@properDivisors@> 1+i.20000

15120 79

18480 79</lang>

Note that it's more efficient to simply count factors here, when selecting the candidate numbers.

<lang J> (, #@properDivisors)&> 1+I.(= >./) #@factors@> 1+i.20000

15120 79

18480 79</lang>

We could also arbitrarily toss either 15120 or 18480, if that were important.