Sphenic number

A sphenic number is a positive integer that is the product of three distinct prime factors. The Möbius function returns −1 when passed any sphenic number.

Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 2² × 3 × 5 has exactly 3 prime factors, but is not sphenic.

All sphenic numbers have exactly eight divisors. If we express the sphenic number as <math>n = x \cdot y \cdot z<math>, then its divisors will be (possibly not sorted):

<math>\left\{ 1, \ x, \ y, \ z, \ x y, \ x z, \ y z, \ n \right\}<math>

The first few sphenic numbers are: 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ...

External links

• Sphenic numbers from On-Line Encyclopedia of Integer Sequences.