A260626 a(n) = gcd(m, 2^m-1) where m is the n-th nonprime positive integer.

1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 5, 7, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 9, 1, 1, 5, 21, 1, 1, 1, 3, 1, 1, 1, 1, 27, 1, 1, 1, 1, 15, 1, 7, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 3, 5, 1, 1, 21, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 3, 1, 1, 25, 3, 1, 7, 1, 27, 11, 1, 1, 3, 1

Offset: 1

Author

Michel Lagneau, Oct 31 2015

Keywords

• nonn
• easy

Comments

2^m - 1 is a nonprime number if m is a nonprime number.

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014491, A018252.

Programs

Maple

seq(`if`(isprime(m), NULL, igcd(m, 2^m-1)), m=1..150);

Mathematica

GCDnonPrime[n_Integer]:=GCD[2^FixedPoint[n+PrimePi@#&,n+PrimePi@n]-1,FixedPoint[n+PrimePi@#&,n+PrimePi@n]];Array[GCDnonPrime,120]
GCD[#,2^#-1]&/@Select[Range[200],!PrimeQ[#]&] (* Harvey P. Dale, Aug 25 2019 *)

PARI

for(n=1, 1e3, if(!isprime(n), print1(gcd(n,2^n-1)", "))) \\ Altug Alkan, Nov 01 2015

Formula

a(n) = gcd(A018252(n), 2^A018252(n)-1).

a(n) = A014491(A018252(n)). - Michel Marcus, Nov 01 2015