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A214606 a(n) = gcd(n, 2^n - 2).

%I A214606 #37 Sep 08 2022 08:46:02
%S A214606 1,2,3,2,5,2,7,2,3,2,11,2,13,2,3,2,17,2,19,2,3,2,23,2,5,2,3,14,29,2,
%T A214606 31,2,3,2,1,2,37,2,3,2,41,2,43,2,15,2,47,2,7,2,3,2,53,2,1,2,3,2,59,2,
%U A214606 61,2,3,2,5,2,67,2,3,14,71,2,73,2,3,2,1,2,79
%N A214606 a(n) = gcd(n, 2^n - 2).
%C A214606 Greatest common divisor of n and 2^n - 2.
%C A214606 a(n)=n iff n=1 or n is prime or n is Fermat pseudoprime to base 2 or even pseudoprime to base 2. - Corrected by _Thomas Ordowski_, Jan 25 2016
%C A214606 Indices of 1's: A121707 preceded by 1. - False, see A267999.
%C A214606 Numbers n such that a(n) does not equal A020639(n) (the least prime factor of n): A146077.
%H A214606 Charles R Greathouse IV, <a href="/A214606/b214606.txt">Table of n, a(n) for n = 1..10000</a>
%e A214606 a(3) = 3 because 2^3 - 2 = 6 and gcd(3, 6) = 3.
%e A214606 a(4) = 2 because 2^4 - 2 = 14 and gcd(4, 14) = 2.
%p A214606 seq(igcd(n, (2&^n - 2) mod n), n=1 .. 1000); # _Robert Israel_, Jan 26 2016
%t A214606 Table[GCD[n, 2^n - 2], {n, 1, 59}] (* _Alonso del Arte_, Jul 22 2012 *)
%o A214606 (Java)
%o A214606 import java.math.BigInteger;
%o A214606 public class A214606 {
%o A214606   public static void main (String[] args) {
%o A214606     BigInteger c1 = BigInteger.valueOf(1);
%o A214606     BigInteger c2 = BigInteger.valueOf(2);
%o A214606     for (int n=0; n<222; n++) {
%o A214606       BigInteger bn=BigInteger.valueOf(n),pm2=c1.shiftLeft(n).subtract(c2);
%o A214606       System.out.printf("%s, ", bn.gcd(pm2).toString());
%o A214606     }
%o A214606   }
%o A214606 }
%o A214606 (PARI) a(n)=gcd(n,lift(Mod(2,n)^n-2)) \\ _Charles R Greathouse IV_, May 29 2014
%o A214606 (Magma) [GCD(n, 2^n-2): n in [1..80]]; // _Vincenzo Librandi_, Jan 26 2016
%Y A214606 Cf. A000918, A064535, A121707, A020639, A146077.
%K A214606 nonn,easy
%O A214606 1,2
%A A214606 _Alex Ratushnyak_, Jul 22 2012