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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..183

Chris Caldwell, Mersenne Primes: History, Theorems and Lists.

Example

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.

Prog

(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]", ")); ) }

Crossrefs

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

Sequence in context: A128872 A263379 A073905 * A145098 A136031 A145097

Adjacent sequences: A089155 A089156 A089157 * A089159 A089160 A089161

Keyword

nonn

Author

Cino Hilliard, Dec 06 2003

Status

approved