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A214606 a(n) = gcd(n, 2^n - 2). 1
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, 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, 61, 2, 3, 2, 5, 2, 67, 2, 3, 14, 71, 2, 73, 2, 3, 2, 1, 2, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Greatest common divisor of n and 2^n - 2.
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
Indices of 1's: A121707 preceded by 1. - False, see A267999.
Numbers n such that a(n) does not equal A020639(n) (the least prime factor of n): A146077.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 3 because 2^3 - 2 = 6 and gcd(3, 6) = 3.
a(4) = 2 because 2^4 - 2 = 14 and gcd(4, 14) = 2.
MAPLE
seq(igcd(n, (2&^n - 2) mod n), n=1 .. 1000); # Robert Israel, Jan 26 2016
MATHEMATICA
Table[GCD[n, 2^n - 2], {n, 1, 59}] (* Alonso del Arte, Jul 22 2012 *)
PROG
(Java)
import java.math.BigInteger;
public class A214606 {
public static void main (String[] args) {
BigInteger c1 = BigInteger.valueOf(1);
BigInteger c2 = BigInteger.valueOf(2);
for (int n=0; n<222; n++) {
BigInteger bn=BigInteger.valueOf(n), pm2=c1.shiftLeft(n).subtract(c2);
System.out.printf("%s, ", bn.gcd(pm2).toString());
}
}
}
(PARI) a(n)=gcd(n, lift(Mod(2, n)^n-2)) \\ Charles R Greathouse IV, May 29 2014
(Magma) [GCD(n, 2^n-2): n in [1..80]]; // Vincenzo Librandi, Jan 26 2016
CROSSREFS
Sequence in context: A092028 A020639 A092067 * A325643 A353270 A356838
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Jul 22 2012
STATUS
approved

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Last modified February 21 02:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)