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%I #22 Jul 11 2024 01:22:12
%S 89,178481,1103,616318177,164511353,9719,4513,69431,3203431780337,
%T 761838257287,48544121,2298041,202029703,57912614113275649087721,
%U 13842607235828485645766393,341117531003194129,3976656429941438590393
%N Second prime factor, if it exists, of Mersenne numbers.
%H Amiram Eldar, <a href="/A089158/b089158.txt">Table of n, a(n) for n = 1..183</a>
%H Chris Caldwell, <a href="https://t5k.org/mersenne/index.html">Mersenne Primes: History, Theorems and Lists</a>.
%e The 5th Mersenne number 2^11 - 1 = 23*89 and 89 is the second prime divisor.
%e The 9th Mersenne number 2^23 - 1 = 47*178481 and 178481 is the second prime divisor.
%e Notice 23, 89 congruent to 1 mod 11 and 47, 178481 congruent to 1 mod 23.
%o (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]",")); ) }
%Y Cf. A001348, A016047, A065341, A089159, A089992, A135978.
%K nonn
%O 1,1
%A _Cino Hilliard_, Dec 06 2003