highly composite number

In the unpublished section of his notebook, Ramanujan extends the notion of highly composite number to other arithmetic functions, mainly to Q_2k(N),1<k<4, where Q_2k(N) denotes the number of representations of N as the sum of 2k squares, and to 𝜎₋ₛ(N), where 𝜎₋ₛ(N) denotes the sum of the (-s)th powers of the divisors of N.

This factorization becomes particularly simple and economical when N is a highly composite number, in particular a power of 2.