A073501 Primes p such that the largest prime factor of p^2+1 is less than p.

7, 41, 43, 47, 73, 83, 157, 173, 191, 193, 211, 233, 239, 251, 293, 307, 313, 337, 401, 421, 431, 443, 463, 467, 499, 509, 557, 577, 593, 599, 601, 659, 701, 743, 757, 787, 811, 829, 853, 857, 863, 911, 919, 1087, 1109, 1123, 1223, 1229, 1277, 1297, 1301

Offset

1,1

Comments

Primes p such that the largest prime factor of p+1 is less than p gives A065091, odd primes.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) max(numtheory:-factorset(n^2+1))<n end proc:
select(filter, [seq(ithprime(i), i=1..1000)]); # Robert Israel, Aug 07 2019

Mathematica

<<NumberTheory`NumberTheoryFunctions` Select[Prime[Range[250]], Max[PrimeFactorList[1 + #^2]] < # &] (* Ray Chandler, Jan 08 2005 *)
Select[Prime[Range[212]], Max[First /@ FactorInteger[#^2 + 1]] < # &] (* Jayanta Basu, Jul 01 2013 *)

Prog

(Magma) [p:p in PrimesUpTo(1500)|Max(PrimeDivisors(p^2+1)) lt p]; // Marius A. Burtea, Aug 07 2019

Crossrefs

Cf. A065091, A073501, A256011.

Sequence in context: A123747 A144421 A023251 * A080666 A224718 A374234

Adjacent sequences: A073498 A073499 A073500 * A073502 A073503 A073504

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 27 2002

Status

approved