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{title2=$S(A,\mathcal P,z)$}

For a finite integer set $A$ and a set of primes $\mathcal P$, the sifting function counts elements of $A$ divisible by no prime in $\mathcal P$ below $z$:
$$
S(A,\mathcal P,z)=\left|\left\{a\in A:\gcd(a,P(z))=1\right\}\right|,
\qquad
P(z)=\prod_{\substack{p\in\mathcal P\\p\leq z}}p.
$$


Sifting function

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 150 / 1 / a / Solution

Sifting function ( $S (A, P, z)$ )

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