# Is there a name for a number that has at most $k$ distinct prime factors?

Purely out of curiosity, is there a name for a positive integer that has at most a given number of distinct prime factors?

Suppose a positive integer $n$ has at most $k$ distinct prime factors. The best word I can think of for this is, perhaps, 'simple,' since at least for small $k$ the prime factorization of a $k$-simple number will not be difficult to write out - that is, will not be a long string of distinct primes. A $2$-simple number will have prime factorization $p^aq^b$ for $p$ and $q$ distinct primes and $a,b \in \mathbb{Z}^+$, a $3$-simple number will be $p^aq^br^c$, and so on.

So for example, $100=2^2\cdot 5^2$ is $2$-simple, $30=2\cdot 3\cdot 5$ is $3$-simple, and $210=2\cdot 3 \cdot 5 \cdot 7$ is $4$-simple. Clearly a number is $1$-simple if and only if it is a prime power.

Is there such a term commonly in use?

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Supported at $k$ primes? –  jspecter Jan 30 at 4:57
–  Brett Frankel Jan 30 at 4:58