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

1600, 2949, 3370, 8651, 8758, 8777, 9308, 9647, 10181, 10566, 10820, 11518, 12400, 12461, 13360, 13724, 14051, 14273, 14971, 16802, 18073, 18283, 18324, 18979, 22143, 22812, 23343, 23766, 24590, 24780, 25152, 25253, 25313, 25897, 26097, 26659, 27106, 27134, 28523, 28526, 29586, 29588, 30660

Offset

1,1

Comments

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

Links

David A. Corneth, Table of n, a(n) for n = 1..7762 (first 1000 terms from Robert Israel)

Example

1600 is a member because 1600^4+1=17^2*113*337*641*929 has all its prime divisors < 1600.

Maple

filter := proc(n) max(numtheory:-factorset(n^4 + 1)) < n; end proc:
select(filter, [$1..40000]);

Mathematica

filterQ[k_] := FactorInteger[k^4 + 1][[-1, 1]] < k;
Select[Range[40000], filterQ] (* Jean-François Alcover, Jul 31 2020 *)

Prog

(Magma) [k: k in [1..31000]| Max(PrimeDivisors(k^4+1)) lt k]; // Marius A. Burtea, Aug 07 2019
(PARI) is(n) = my(f = factor(n^4 + 1, n + 1)); f[#f~, 1] < n \\ David A. Corneth, Jul 31 2020

Crossrefs

Cf. A102326 (primes in this sequence), A256011.

Sequence in context: A252110 A224951 A260499 * A043412 A202096 A258675

Adjacent sequences: A309559 A309560 A309561 * A309563 A309564 A309565

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 07 2019

Status

approved