Sphenic number

A sphenic number (Old Greek sphen = wedge) 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 n = x \cdot y \cdot z, then its divisors will be (possibly not sorted):

\left\{ 1, \ x, \ y, \ z, \ x y, \ x z, \ y z, \ n \right\}

The first few sphenic numbers are: 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, ...

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See also: Sphenic number, -1 (number), 102 (number), 105 (number), 110 (number), 114 (number), 130 (number), 138 (number)