A089159 - OEIS

%I #20 Jul 11 2024 01:21:59

%S 2089,2099863,13264529,20394401,212885833,9361973132609,1113491139767,

%T 65993,165799,1654058017289,110211473,70084436712553223,

%U 1489459109360039866456940197095433721664951999121,7648337,39940132241,14732265321145317331353282383

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

%H Amiram Eldar, <a href="/A089159/b089159.txt">Table of n, a(n) for n = 1..144</a>

%H Chris Caldwell, <a href="https://t5k.org/mersenne/index.html">Mersenne Primes: History, Theorems and Lists</a>.

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

%e 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).

%o (PARI) mersenne2(n) = { c=0; forprime(x=2, n, c++; y = 2^x-1; f=ifactor(y); if(length(f)>=3, print1(f[3]","); ) ) }

%o 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) }

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

%K nonn

%O 1,1

%A _Cino Hilliard_, Dec 06 2003, corrected Nov 16 2006

%E a(16) from _Amiram Eldar_, Jul 11 2024