In the number analogy 12 : 16 :: 18 : ?, which value replaces the question mark?

Every whole number that divides the given number, the number itself excepted, is added up. For 12 those divisors are 1, 2, 3, 4 and 6, totalling 16. For 18 they are 1, 2, 3, 6 and 9, totalling 21. The trap 39 counts 18 itself into the total, but doing that to 12 gives 28 and not 16. 20 leaves the 1 out, which on the first pair yields 15, and 36 simply doubles the number, against 24 the first time.