**distinct prime factor counting function**is the D5406: Positive integer function \begin{equation} \{ 2, 3, 4, \ldots \} \to \{ 1, 2, 3, \ldots \}, \quad \prod_{n = 1}^N p_n^{a_n} \mapsto N \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Ringoid

▾ Semiring

▾ Ring

▾ Factor

▾ Divisor

▾ Two-sided divisor

▾ Prime element

▾ Set of prime elements

▾ Prime factorisation

▾ Prime integer factorisation

▾ Prime integer power factorisation

▾ Prime factor counting function

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Ringoid

▾ Semiring

▾ Ring

▾ Factor

▾ Divisor

▾ Two-sided divisor

▾ Prime element

▾ Set of prime elements

▾ Prime factorisation

▾ Prime integer factorisation

▾ Prime integer power factorisation

▾ Prime factor counting function

Formulation 0

The **distinct prime factor counting function** is the D5406: Positive integer function
\begin{equation}
\{ 2, 3, 4, \ldots \} \to \{ 1, 2, 3, \ldots \}, \quad
\prod_{n = 1}^N p_n^{a_n} \mapsto N
\end{equation}