A194099 - OEIS

%I #43 Nov 11 2016 07:42:08

%S 3,5,7,11,17,19,29,31,41,49,71,161,251,449,769,881,1079,1429,3431,

%T 4159,4801,6049,8749,19601,24751,246401,388961,1267111

%N Numbers m>=2, such that, if a prime p divides m^2-1, then every prime q<p divides m^2-1 as well.

%C No more terms <= 10^8.

%C No more terms <= 2 * 10^38. [_Charles R Greathouse IV_, Aug 22 2011]

%C All terms are odd. - _Kausthub Gudipati_, Aug 22 2011

%H Florian Luca and Filip Najman, <a href="https://web.math.pmf.unizg.hr/~fnajman/FLFNMC.pdf">On the largest prime factor of x^2 - 1.</a> Math. Comp. 80 (2011), 429-435.

%F A055932 INTERSECT A005563. - _R. J. Mathar_, Aug 16 2011

%e 881^2-1 = 776160 = 2^5 * 3^2 * 5 *7^2 * 11 (all primes <= 11 appear), so 881 is a term.

%t Select[Range[1, 10^4], First@ # == 1 && If[Length@ # > 1, Union@ Differences@ # == {1}, True] &@ PrimePi@ Map[First, FactorInteger[#^2 - 1]] &] (* _Michael De Vlieger_, Jul 02 2016 *)

%o (PARI) isok(n) = my(f = factor(n^2-1)); #f~ == primepi(f[#f~,1]); \\ _Michel Marcus_, Jul 02 2016

%Y Cf. A005563, A055932.

%K nonn,more

%O 1,1

%A _Vladimir Shevelev_, Aug 15 2011