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 , where p, q, and r are distinct primes, then the set of divisors of n will be:
All sphenic numbers are by definition squarefree, because the prime factors must be distinct.
The Möbius function of any sphenic number is −1.
The first case of two consecutive integers which are sphenic numbers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17, 1310 = 2×5×131, and 1311 = 3×19×23. There is no case of more than three, because one of every four consecutive integers is divisible by 4 = 2×2 and therefore not squarefree. the largest known sphenic number is (243,112,609 − 1) × (237,156,667 − 1) × (232,582,657 − 1), i.e., the product of the three largest known primes.
Wipo Publishes Patent of Sphenic Technologies, Plotnikov Alexandre for "System, Circuit and Method for Controlling Combustion" (Canadian Inventors)
Aug 20, 2012; GENEVA, Aug. 20 -- Publication No. WO/2012/106807 was published on Aug. 16. Title of the invention: "SYSTEM, CIRCUIT, AND METHOD...