When calculating slugging percentage, why do the numbers of singles, doubles, and triples get multiplied by 2, 3 and 4, respectively, in the numerator? And, perhaps related, why does the HR count remain as is without a coefficient?
I think you just have the definition of slugging percentage wrong. Quoting from Wikipedia:
[Slugging percentage] is calculated as total bases divided by at bats
SLG = ((1B) + (2 x 2B) + (3 x 3B) + (4 x HR)) / AB
i.e. singles are multiplied by one (not two), doubles by two (not three), triples by three (not four) and home runs by four (not one).