Last Updated：2025/12/31
Sentence
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unpublished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.
Quizzes for review
In the unpublished section of his notebook, Ramanujan extends the notion of highly composite number to other arithmetic functions, mainly to Q_2k(N),1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.
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