## Carmichael number, more or less

**A** quick-and-dirty R resolution of a riddle from The Riddler, namely to find a Carmichael number of the form abcabc:

library(numbers) for(i in 1:9) for(j in 0:9) for(k in 0:9){ x=i*100100+j*1010+k*101 if(!isPrime(x)){ p=primeFactors(x) if((prod(apply(outer(p,p,F="=="),1,sum)%%2))& (!max((x-1)%%(p-1))))break()}}

resulting into the number 101 101, since its prime factors are

> primeFactors(101101) [1] 7 11 13 101

and 6, 10, 12, and 100 are divisors of 101100:

> primeFactors(101100) [1] 2 2 3 5 5 337

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