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Primes p such that all prime divisors of p^2 + p + 1 are less than p.
2

%I #12 Feb 13 2016 15:22:36

%S 67,79,137,149,163,181,191,211,229,263,269,277,313,373,431,439,499,

%T 521,571,631,653,787,809,811,821,823,919,947,971,991,997,1049,1069,

%U 1087,1109,1129,1153,1231,1237,1283,1291,1367,1429,1451,1459,1471,1493,1511

%N Primes p such that all prime divisors of p^2 + p + 1 are less than p.

%H R. J. Mathar, <a href="/A091490/b091490.txt">Table of n, a(n) for n = 1..4725</a>

%H Robin Chapman, <a href="https://groups.google.com/forum/#!topic/sci.math/CPnCgxBE6Ek">Comments on the Somon Davis paper</a>

%H Simon Davis, <a href="http://arXiv.org/abs/hep-th/0401052">A Proof of the Odd Perfect Number Conjecture</a>, arXiv:hep-th/0401052 [But see the comments on this paper by Robin Chapman]

%t PrimeFactors[ n_Integer ] := Flatten[ Table[ #[ [ 1 ] ], {1} ] & /@ FactorInteger[ n ] ]; Prime[ Select[ Range[ 242 ], Prime[ # ] > PrimeFactors[ Prime[ # ]^2 + Prime[ # ] + 1 ][ [ -1 ] ] & ] ]

%Y Cf. A073501.

%K nonn

%O 1,1

%A _R. K. Guy_ and _Robert G. Wilson v_, Jan 14 2004