A214093 Largest prime p such that the greatest prime factor of p^2-1 is prime(n).
3, 17, 31, 4801, 881, 8191, 388961, 1419263, 4046849, 36171409, 4620799, 617831551, 170918749, 842277599279, 3554663111, 187753824257, 19854354911, 1233008445689, 60292968751, 508070657249, 4421151404801, 259476225058051, 17431549081705001, 45163738135361, 99913980938200001
Offset: 1
Examples
a(6)=8191 because 8190 = 2*3^2*5*7*13, 8192=2^13 and prime(6)=13.
Links
- Filip Najman, Home Page (gives all numbers n such that n^2-1 has no prime factor greater than 97)
Crossrefs
Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).
Programs
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PARI
/* up to term for p=97 */ /* S[] is the list computed by Filip Najman (16223 elements) */ S=[2, 3, 4, ... , 332110803172167361, 19182937474703818751]; lpf(n)={ vecmax(factor(n)[, 1]) } /* largest prime factor */ { forprime (p=2, 97, t = 0; for (n=1,#S, if ( lpf(S[n]^2-1)==p && isprime(S[n]), t=n ); ); print1(S[t],", "); );}
Comments