Summatory function
= Summatory function
{title2=$A(x)=\sum_{n\le x}a(n)$}
The summatory function of an <arithmetic function> $a$ is $A(x)=\sum_{1\le n\le x}a(n)$. For example, the <prime-counting function> sums the indicator of the <prime numbers>, while the <divisor summatory function> sums the <divisor function>. Grouping equal values of $\lfloor x/d\rfloor$ often speeds up identities involving summatory functions.