A375322 - OEIS

%I #18 Sep 01 2024 16:50:35

%S 1729,6601,10585,15841,41041,46657,658801,1461241,1615681,1857241,

%T 2433601,3057601,3581761,4767841,5031181,5148001,6840001,7207201,

%U 8355841,10024561,10402561,14469841,14676481,17236801,17316001,19683001,25603201,35571601,35703361,38624041

%N Carmichael numbers k such that k-1 is a Novak-Carmichael number.

%C Composite numbers k such that lambda(k) divides k-1 and lambda(k-1) divides k-1, where lambda(m) = A002322(m).

%C These are composites k such that b^(k-1) == 1 (mod (k-1)*k) for every b coprime to (k-1)*k.

%C Composites k such that B^(b^(k-1)-1) == 1 (mod k^2) for every B coprime to k and for every b coprime to (k-1)*k.

%H Amiram Eldar, <a href="/A375322/b375322.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[1, 10^6, 2], CompositeQ[#] && And @@ Divisible[# - 1, CarmichaelLambda[# + {-1, 0}]] &] (* _Amiram Eldar_, Aug 12 2024 *)

%o (PARI) f(n) = lcm(znstar(n)[2]); \\ A002322

%o isok(k) = !isprime(k) && !((k-1) % f(k)) && !((k-1) % f(k-1)); \\ _Michel Marcus_, Aug 13 2024

%Y Cf. A002322, A002997, A124240 (Novak-Carmichael numbers), A337119.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Aug 12 2024

%E More terms from _Amiram Eldar_, Aug 12 2024