OFFSET
1,1
COMMENTS
These are composites k such that lambda(k^2) divides k(k-1), where lambda is the Carmichael function A002322.
Since lambda(p^2) = phi(p^2) = p(p-1), where p is a prime, then by Euler's theorem b^(p(p-1)) == 1 (mod p^2) for every b indivisible by p.
This sequence includes all Carmichael numbers A002997.
Conjecture: all semiprimes > 4 in this sequence are in A190275. - Thomas Ordowski, Jul 19 2020
The conjecture was verified up to 1063290841. - Amiram Eldar, Jul 19 2020
MATHEMATICA
Select[Range[2000], CompositeQ[#] && Divisible[#(#-1), CarmichaelLambda[#^2]] &]
PROG
(PARI) isok(k) = (k!=1) && !isprime(k) && !(k*(k-1) % lcm(znstar(k^2)[2])); \\ Michel Marcus, Mar 12 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar and Thomas Ordowski, Feb 01 2019
STATUS
approved