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URL: https://oeis.org/A375322

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A375322
Carmichael numbers k such that k-1 is a Novak-Carmichael number.
1
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
1,1
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
MATHEMATICA
Select[Range[1, 10^6, 2], CompositeQ[#] && And @@ Divisible[# - 1, CarmichaelLambda[# + {-1, 0}]] &] (* Amiram Eldar, Aug 12 2024 *)
PROG
(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
CROSSREFS
Cf. A002322, A002997, A124240 (Novak-Carmichael numbers), A337119.
Sequence in context: A130859 A245671 A154716 * A154728 A286217 A382809
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Aug 12 2024
EXTENSIONS
More terms from Amiram Eldar, Aug 12 2024
STATUS
approved