A089159 If Mersenne numbers have 3 or more factors, then list the third factor.

2089, 2099863, 13264529, 20394401, 212885833, 9361973132609, 1113491139767, 65993, 165799, 1654058017289, 110211473, 70084436712553223, 1489459109360039866456940197095433721664951999121, 7648337, 39940132241, 14732265321145317331353282383

Offset: 1

Author

Cino Hilliard, Dec 06 2003, corrected Nov 16 2006

Keywords

• nonn

Examples

			The 10th Mersenne number 2^29 - 1 = 233*1103*2089 and 2089 is the third prime factor. Notice these factors are congruent to 1 (mod 29).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..144
• Chris Caldwell, Mersenne Primes: History, Theorems and Lists.

Crossrefs

Cf. A000043, A001348, A016047, A089158, A135977, A344515.

Programs

PARI

mersenne2(n) = { c=0; forprime(x=2, n, c++; y = 2^x-1; f=ifactor(y); if(length(f)>=3, print1(f[3]","); ) ) }
ifactor(n) = { local(f,j,k,flist); flist=[]; f=Vec(factor(n)); for(j=1,length(f[1]), for(k = 1,f[2][j],flist = concat(flist,f[1][j]) ); ); return(flist) }

Formula

A Mersenne number (A001348) is a number of the form 2^p - 1 where p is prime.

Extensions

a(16) from Amiram Eldar, Jul 11 2024