A153513 Composite numbers k such that 2^k-2 and 3^k-3 are both divisible by k and k is not a Carmichael number (A002997).

2701, 18721, 31621, 49141, 83333, 83665, 88561, 90751, 93961, 104653, 107185, 176149, 204001, 226801, 228241, 276013, 282133, 534061, 563473, 574561, 622909, 653333, 665281

Offset: 1

Author

Artur Jasinski, Dec 28 2008

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..200 from Robert Israel)

Crossrefs

Intersection of A153514 and A153508 (excluding the number 1).

Cf. A002997, A122780.

Programs

Maple

filter:= proc(n) local p;
  if isprime(n) or (2 &^n - 2 mod n <> 0) or (3 &^n - 3 mod n <> 0) then return false fi;
  if n::even then return true fi;
  if not numtheory:-issqrfree(n) then return true fi;
  for p in numtheory:-factorset(n) do
    if n-1 mod (p-1) <> 0 then return true fi
  od;
false
end proc:
select(filter, [$2..10^6]); # Robert Israel, Jan 29 2017

Mathematica

Reap[Do[If[CompositeQ[n] && Divisible[2^n-2, n] && Divisible[3^n-3, n] && Mod[n, CarmichaelLambda[n]] != 1, Print[n]; Sow[n]], {n, 2, 10^6}]][[2, 1]] (* Jean-François Alcover, Mar 25 2019 *)