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Completely additive arithmetic function
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Number theory
Arithmetic function
Additive function (number theory)
Created
2026-10-06
Updated
2026-10-14
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A
completely additive arithmetic function
satisfies
f
(
mn
)
=
f
(
m
)
+
f
(
n
)
for all positive
m
,
n
, equivalently
f
(
p
k
)
=
k
f
(
p
)
. The
total number of prime factors
is an example.
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(6)
Additive function (number theory)
Arithmetic function
Number theory
Area of mathematics
Mathematics
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Completely additive arithmetic function
Past exam of the mathematics course of the University of Cambridge
/
2016
/
iii
/
Paper 124
/
1
/
a
/
Solution
Prime omega function
Total number of prime factors
Synonyms
(1)
codex/completely-additive-function
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