A375322 Carmichael numbers k such that k-1 is a Novak-Carmichael number.

1729, 6601, 10585, 15841, 41041, 46657, 658801, 1461241, 1615681, 1857241, 2433601, 3057601, 3581761, 4767841, 5031181, 5148001, 6840001, 7207201, 8355841, 10024561, 10402561, 14469841, 14676481, 17236801, 17316001, 19683001, 25603201, 35571601, 35703361, 38624041

Offset: 1

Author

Thomas Ordowski, Aug 12 2024

Keywords

• nonn

Comments

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

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

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

PARI

f(n) = lcm(znstar(n)[2]); \\ A002322
isok(k) = !isprime(k) && !((k-1) % f(k)) && !((k-1) % f(k-1)); \\ Michel Marcus, Aug 13 2024

Extensions

More terms from Amiram Eldar, Aug 12 2024