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%I #5 Mar 30 2012 17:30:50
%S 9,27,2187,19683,300763,1092727,2048383,6128487
%N Perfect powers n such that (n-5)/2 is prime.
%e 9=3^2, 27=3^3, 2187=3^7, 19683=3^9, but 300763=67^3 - is there any rule?
%t pp = Join[{1}, Select[ Range[10^7], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[(# - 5)/2] & ]
%K easy,nonn
%O 1,1
%A _Zak Seidov_, Oct 11 2002
%E Extended by _Robert G. Wilson v_, Oct 14 2002