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## Four integer sequences

In this challenge, you will test four different properties of a positive integer, given by the following sequences.
A positive integer **N** is

*perfect*(OEIS A000396), if the sum of proper divisors of**N**equals**N**. The sequence begins with 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128...*refactorable*(OEIS A033950), if the number of divisors of**N**is a divisor of**N**. The sequence begins with 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96, 104, 108, 128...*practical*(OEIS A005153), if every integer**1 ≤ K ≤ N**is a sum of some distinct divisors of**N**. The sequence begins with 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56...*highly composite*(OEIS A002128), if every number**1 ≤ K < N**has strictly fewer divisors than**N**. The sequence begins with 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040...

## Four programs

Your task is to write four programs (meaning full programs, function definitions or anonymous functions that perform I/O by any of the standard methods).
Each program shall solve the membership problem of one of these sequences.
In other words, each program will take a positive integer **N ≥ 1** as input, and output a truthy value if **N** is in the sequence, and a falsy value if not.
You can assume that **N** is within the bounds of the standard integer type of your programming language.

The programs must be related in the following way.
There are four strings `ABCD`

such that

`AC`

is the program that recognizes perfect numbers.`AD`

is the program that recognizes refactorable numbers.`BC`

is the program that recognizes practical numbers.`BD`

is the program that recognizes highly composite numbers.

## Scoring

Your score is the total length (in bytes) of the strings `ABCD`

, or in other words, the total byte count of the four programs divided by two.
The lowest score in each programming language is the winner.
Standard code-golf rules apply.

For example, if the four strings are `a{`

, `b{n`

, `+n}`

and `=n}?`

, then the four programs are `a{+n}`

, `a{=n}?`

, `b{n+n}`

and `b{n=n}?`

, and the score is 2+3+3+4=12.

Related, Related, Related. – Mr. Xcoder – 2018-03-17T14:26:49.300