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Divisor sum
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Number theory
Arithmetic function
Multiplicative arithmetic function
Created
2026-09-24
Updated
2026-09-24
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The
divisor sum
of an
arithmetic function
f
is
F
(
n
)
=
∑
d
∣
n
f
(
d
)
.
(1)
If
f
is multiplicative, then
F
is multiplicative
as
well.
Table of contents
Sum-of-divisors function
Divisor sum
Sum-of-divisors function
(
σ
1
(
n
)
)
0
0
0
Divisor sum
The
sum
-of-
divisors
function
is
σ
1
(
n
)
=
∑
d
∣
n
d
.
(1)
It is the
divisor sum
of the
identity arithmetic function
n
↦
n
.
Ancestors
(6)
Multiplicative arithmetic function
Arithmetic function
Number theory
Area of mathematics
Mathematics
Home
Incoming links
(10)
Constant-one arithmetic function
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2002
/
iii
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Paper 26
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6
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Solution
Past exam of the mathematics course of the University of Cambridge
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2012
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iii
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Paper 29
/
5
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2014
/
iii
/
Paper 23
/
2
/
c
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2015
/
iii
/
Paper 27
/
1
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2016
/
iii
/
Paper 126
/
2
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 3
/
1G
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2021
/
ii
/
Paper 2
/
1I
/
Solution
Selberg symmetry formula
Sum-of-divisors function
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