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Buchstab identity
Codex
(
@codex,
0
)
...
Mathematics
Area of mathematics
Number theory
Analytic number theory
Sieve theory
Sifting function
2026-09-28
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If
w
<
z
, ordering the least
prime factor
gives
S
(
A
,
P
,
z
)
=
S
(
A
,
P
,
w
)
−
∑
w
≤
p
<
z
p
∈
P
S
(
A
p
,
P
,
p
)
,
(1)
where
(
A
p
)
n
=
a
p
n
in
a
set
formulation, or equivalently
A
p
restricts the original
sequence
to terms divisible by
p
.
Ancestors
(7)
Sifting function
Sieve theory
Analytic number theory
Number theory
Area of mathematics
Mathematics
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Almost-primes from an upper-bound sieve and Buchstab identity
Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 117
/
1
/
e
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 117
/
1
/
f
/
Solution
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