Lucas-Carmichael number

Given an odd squarefreeMathworldPlanetmath integer n (that is, one with factorization n=i=1ω(n)pi, with ω(n) being the number of distinct prime factors function, and all pi>2) if it the case that each pi+1 is a divisorMathworldPlanetmathPlanetmath of n+1, then n is called a Lucas-Carmichael number.

For example, 935 has three prime factorsMathworldPlanetmath, 5, 11, 17. Adding one to each of these we get 6, 12, 18, and these three numbers are all divisors of 936. Therefore, 935 is a Lucas-Carmichael number.

The first few Lucas-Carmichael numbers are 399, 935, 2015, 2915, 4991, 5719, 7055, 8855. These are listed in A006972 of Sloane’s OEIS.

Not to be confused with Carmichael numbersMathworldPlanetmath, the absolute Fermat pseudoprimes.

Title Lucas-Carmichael number
Canonical name LucasCarmichaelNumber
Date of creation 2013-03-22 17:41:14
Last modified on 2013-03-22 17:41:14
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51