A214093 - OEIS

%I #9 Apr 02 2013 17:15:30

%S 3,17,31,4801,881,8191,388961,1419263,4046849,36171409,4620799,

%T 617831551,170918749,842277599279,3554663111,187753824257,19854354911,

%U 1233008445689,60292968751,508070657249,4421151404801,259476225058051,17431549081705001,45163738135361,99913980938200001

%N Largest prime p such that the greatest prime factor of p^2-1 is prime(n).

%C The terms were computed using Filip Najman's list, see the link.

%H Filip Najman, <a href="http://web.math.hr/~fnajman/">Home Page</a> (gives all numbers n such that n^2-1 has no prime factor greater than 97)

%e a(6)=8191 because 8190 = 2*3^2*5*7*13, 8192=2^13 and prime(6)=13.

%o (PARI)

%o /* up to term for p=97 */

%o /* S[] is the list computed by Filip Najman (16223 elements) */

%o S=[2, 3, 4, ... , 332110803172167361, 19182937474703818751];

%o lpf(n)={ vecmax(factor(n)[, 1]) } /* largest prime factor */

%o { forprime (p=2, 97,

%o   t = 0;

%o   for (n=1,#S, if ( lpf(S[n]^2-1)==p && isprime(S[n]), t=n ); );

%o   print1(S[t],", ");

%o );}

%Y Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).

%K nonn,hard

%O 1,1

%A _Joerg Arndt_, Jul 03 2012