A089158 Second prime factor, if it exists, of Mersenne numbers.

89, 178481, 1103, 616318177, 164511353, 9719, 4513, 69431, 3203431780337, 761838257287, 48544121, 2298041, 202029703, 57912614113275649087721, 13842607235828485645766393, 341117531003194129, 3976656429941438590393

Offset: 1

Author

Cino Hilliard, Dec 06 2003

Keywords

• nonn

Examples

			The 5th Mersenne number 2^11 - 1 = 23*89 and 89 is the second prime divisor.
The 9th Mersenne number 2^23 - 1 = 47*178481 and 178481 is the second prime divisor.
Notice 23, 89 congruent to 1 mod 11 and 47, 178481 congruent to 1 mod 23.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..183
• Chris Caldwell, Mersenne Primes: History, Theorems and Lists.

Crossrefs

Cf. A001348, A016047, A065341, A089159, A089992, A135978.

Programs

PARI

mersenne(b,n,d) = { c=0; forprime(x=2,n, c++; y = b^x-1; f=factor(y); v=component(f,1); ln = length(v); if(ln>=d,print1(v[d]",")); ) }