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

1,1

Links

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

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 *)

Crossrefs

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

Cf. A002997, A122780.

Sequence in context: A230752 A364795 A246888 * A333130 A214016 A254513

Adjacent sequences: A153510 A153511 A153512 * A153514 A153515 A153516

Keyword

nonn

Author

Artur Jasinski, Dec 28 2008

Status

approved