cp's OEIS Frontend

A309562 Numbers k such that the largest prime divisor of k^4+1 is less than k.

%I A309562 #24 Sep 08 2022 08:46:21
%S A309562 1600,2949,3370,8651,8758,8777,9308,9647,10181,10566,10820,11518,
%T A309562 12400,12461,13360,13724,14051,14273,14971,16802,18073,18283,18324,
%U A309562 18979,22143,22812,23343,23766,24590,24780,25152,25253,25313,25897,26097,26659,27106,27134,28523,28526,29586,29588,30660
%N A309562 Numbers k such that the largest prime divisor of k^4+1 is less than k.
%C A309562 To see if some m is a term we don't have to factor m^4 + 1 entirely. All we need to know is if the largest prime factor is less than k = m^4 + 1. - _David A. Corneth_, Jul 31 2020
%H A309562 David A. Corneth, <a href="/A309562/b309562.txt">Table of n, a(n) for n = 1..7762</a> (first 1000 terms from Robert Israel)
%e A309562 1600 is a member because 1600^4+1=17^2*113*337*641*929 has all its prime divisors < 1600.
%p A309562 filter := proc(n) max(numtheory:-factorset(n^4 + 1)) < n; end proc:
%p A309562 select(filter, [$1..40000]);
%t A309562 filterQ[k_] := FactorInteger[k^4 + 1][[-1, 1]] < k;
%t A309562 Select[Range[40000], filterQ] (* _Jean-François Alcover_, Jul 31 2020 *)
%o A309562 (Magma) [k: k in [1..31000]| Max(PrimeDivisors(k^4+1)) lt k]; // _Marius A. Burtea_, Aug 07 2019
%o A309562 (PARI) is(n) = my(f = factor(n^4 + 1, n + 1)); f[#f~, 1] < n \\ _David A. Corneth_, Jul 31 2020
%Y A309562 Cf. A102326 (primes in this sequence), A256011.
%K A309562 nonn
%O A309562 1,1
%A A309562 _J. M. Bergot_ and _Robert Israel_, Aug 07 2019