Lucas-Carmichael number

Given an odd squarefree integer $n$ (that is, one with factorization $\\displaystyle n=\\prod_{i=1}^{\\omega(n)}p_{i}$ , with $\\omega(n)$ being the number of distinct prime factors function, and all $p_{i}>2$ ) if it the case that each $p_{i}+1$ is a divisor of $n+1$ , then $n$ is called a Lucas-Carmichael number.

For example, 935 has three prime factors, 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 numbers, the absolute Fermat pseudoprimes.

单词	LucasCarmichaelNumber
释义	Lucas-Carmichael number Given an odd squarefree integer $n$ (that is, one with factorization $\\displaystyle n=\\prod_{i=1}^{\\omega(n)}p_{i}$ , with $\\omega(n)$ being the number of distinct prime factors function, and all $p_{i}>2$ ) if it the case that each $p_{i}+1$ is a divisor of $n+1$ , then $n$ is called a Lucas-Carmichael number. For example, 935 has three prime factors, 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 numbers, the absolute Fermat pseudoprimes.
随便看	harmonic conjugate function HarmonicDivision harmonic division HarmonicFunction harmonic function harmonic function HarmonicFunction1 HarmonicMean harmonic mean HarmonicMeanInTrapezoid harmonic mean in trapezoid HarmonicNumber harmonic number HarmonicOscillator harmonic oscillator HarmonicSeries harmonic series HarnacksPrinciple HarnackTheorem Harnack theorem Harnack’s principle HarshadNumber Harshad number HartigsQuantifier HartleyFunction