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%I #12 Feb 11 2019 22:01:47
%S 27,243,343,19683,29791,300763,421875,493039,658503,759375,1367631,
%T 2048383,2685619,3176523,4019679,5000211,8869743,9393931,15069223,
%U 17373979,19034163,25672375,32461759,43243551,52734375,54439939,63521199,82312875,84604519
%N Perfect powers n such that (n-17)/2 is prime.
%H Charlie Neder, <a href="/A075548/b075548.txt">Table of n, a(n) for n = 1..865</a>
%e a(1)=3^3, a(2)=3^5, a(3)=7^3, a(4)=3^9, a(5)=31^3, a(6)=67^3, a(7)=75^3, a(8)=79^3, a(9)=87^3, a(10)=15^5, a(11)=111^3, a(12)=127^3, a(13)=139^3, a(14)=147^3, a(15)=159^3, a(16)=171^3, a(17)=207^3 and a(18)=211^3.
%t pp = Join[{1}, Select[ Range[10^7], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[(# - 17)/2] & ]
%t Select[Flatten[Table[n^Range[2,10],{n,250}]],PrimeQ[(#-17)/2]&]//Union (* _Harvey P. Dale_, Dec 08 2018 *)
%K easy,nonn
%O 1,1
%A _Zak Seidov_, Oct 11 2002
%E Extended by _Robert G. Wilson v_, Oct 14 2002
%E a(19)-a(29) from _Charlie Neder_, Feb 11 2019
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