A317210 Composite numbers k+1 such that A002322(A027760(k)) = k.

21, 45, 49, 81, 85, 91, 93, 111, 117, 121, 133, 141, 145, 165, 175, 177, 201, 205, 209, 213, 217, 221, 231, 235, 247, 253, 261, 265, 273, 289, 291, 301, 309, 319, 325, 333, 357, 361, 365, 369, 381, 391, 411, 415, 441, 445, 451, 453, 465, 469, 477, 481, 493

Offset: 1

Author

Max Alekseyev and Thomas Ordowski, Jul 09 2018

Keywords

• nonn

Comments

Also, composite numbers n such that LCM( p-1 : prime p|A027642(n-1) ) = n-1. Also, composite numbers n such that LCM( p-1 : p is prime & (p-1)|(n-1) ) = n-1. - Max Alekseyev, Dec 03 2021

Contains all Carmichael numbers except 2628073, 3224065, 23382529, 182356993, 1419339691, ...

Links

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

Crossrefs

Cf. A027760, A002322.

Programs

Mathematica

1 + Select[Range[500], CompositeQ[# + 1] && CarmichaelLambda[ Times @@ Select[1 + Divisors@ #, PrimeQ]] == # &] (* Giovanni Resta, Aug 13 2018 *)

PARI

a027760(n) = denominator(sumdiv(n, d, if(isprime(d+1), 1/(d+1))));
a002322(n) = lcm(znstar(n)[2]);
isok(n) = !isprime(n) && (n--) && !frac(a002322(a027760(n))/n); \\ Michel Marcus, Aug 13 2018

Extensions

More terms from Giovanni Resta, Aug 13 2018