Sphenic number
From Academic Kids
A sphenic number (Old Greek sphen = wedge) is a positive integer that is the product of three distinct prime factors. The Möbius function returns Template:Num/neg 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, 138, 154, ...
External links
- Sphenic numbers (http://www.research.att.com/projects/OEIS?Anum=A007304) from On-Line Encyclopedia of Integer Sequences.
Template:Math-stubfr:Nombre sphénique it:Numero sfenico he:מספר ספני nl:Sphenisch getal pt:Número esfênico sl:Klinasto število
