sphenic number

Given three primes , the composite integer $pqr$ is a sphenic number. The first few sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, $\mathrm{\dots }$ listed in A007304 of Sloane’s OEIS.

The divisors of a sphenic number therefore are $1,p,q,r,pq,pr,qr,pqr$. Furthermore, $\mu (pqr)={(-1)}^3$ (where $\mu$ is the Möbius function), $\tau (pqr)=8$ (where $\tau$ is the divisor function) and $\mathrm{\Omega }(pqr)=\omega (pqr)=3$ (where $\mathrm{\Omega }$ and $\omega$ are the number of (nondistinct) prime factors function (http://planetmath.org/NumberOfNondistinctPrimeFactorsFunction) and the number of distinct prime factors function, respectively).

The largest known sphenic number at any time is usually the product of the three largest known Mersenne primes.