|
|
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
Numbers n such that a(n) does not equal A020639(n) (the least prime factor of n): A146077.
|
|
LINKS
|
|
|
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
|
|
|
PROG
|
(Java)
import java.math.BigInteger;
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());
}
}
}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|