A089158 -id:A089158 - cp's OEIS frontend

A136031 Largest prime factor of composite Mersenne numbers.

89, 178481, 2089, 616318177, 164511353, 2099863, 13264529, 20394401, 3203431780337, 761838257287, 212885833, 9361973132609, 1113491139767, 57912614113275649087721, 13842607235828485645766393, 341117531003194129, 3976656429941438590393

Offset: 1

Artur Jasinski, Dec 11 2007

nonn

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

Cf. A049479, A016047, A003260, A136030.

FactorInteger[2^#-1][[-1,1]]&/@Select[Prime[Range[40]],!PrimeQ[2^#-1]&] (* Harvey P. Dale, May 05 2012 *)
With[{c=Complement[Prime[Range[PrimePi[200]]],MersennePrimeExponent[ Range[ 15]]]},Table[ FactorInteger[ 2^p-1][[-1,1]],{p,c}]] (* Harvey P. Dale, Sep 06 2021 *)

a(n) >= A089158(n). - R. J. Mathar, May 01 2008

Corrected by Harvey P. Dale, May 05 2012

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

Original entry on oeis.org

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

Offset: 1

Cino Hilliard, Dec 06 2003, corrected Nov 16 2006

nonn

			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).

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

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

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) }

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

a(16) from Amiram Eldar, Jul 11 2024

cp's OEIS Frontend

A136031 Largest prime factor of composite Mersenne numbers.

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