Characteristic functions

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A characteristic function (or indicator function)

${\chi }_A(x)\equiv {\chi }_{p(A)}(x)\equiv {\mathbf{𝐈}}_A(x)\equiv {\mathbf{𝐈}}_{p(A)}(x)$

returns 1 if $x$ has the defining property $p(A)$ of a given set $A$ or 0 otherwise.

For example, the characteristic function of the primes ${\chi }_{\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}}(n)=[\mathrm{\Omega }(n)=1]=\pi (n)-\pi (n-1)$ yields 1 only when $n$ is prime (see A010051). Another example is the characteristic function of squarefree numbers $q(n)=|\mu (n)|$ (see A008966).

See Index to OEIS: Section Ch for a thorough listing of characteristic function sequences in the OEIS.