sphenic number

Given three primes p<q<r, the composite integer pqr is a sphenic numberMathworldPlanetmath. The first few sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, listed in A007304 of Sloane’s OEIS.

The divisorsMathworldPlanetmathPlanetmath of a sphenic number therefore are 1,p,q,r,pq,pr,qr,pqr. Furthermore, μ(pqr)=(-1)3 (where μ is the Möbius functionMathworldPlanetmath), τ(pqr)=8 (where τ is the divisor functionDlmfDlmfMathworldPlanetmath) and Ω(pqr)=ω(pqr)=3 (where Ω and ω are the number of (nondistinct) prime factorsMathworldPlanetmath 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 primesMathworldPlanetmath.

Title sphenic number
Canonical name SphenicNumber
Date of creation 2013-03-22 16:10:33
Last modified on 2013-03-22 16:10:33
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 7
Author CompositeFan (12809)
Entry type Definition
Classification msc 11A05