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A073501
Primes p such that the largest prime factor of p^2+1 is less than p.
7
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
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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 27 2002
STATUS
approved