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%I #9 Feb 11 2019 22:01:31
%S 343,1331,12167,29791,42875,79507,103823,300763,357911,857375,1520875,
%T 2248091,2924207,6436343,9393931,11089567,11697083,15069223,15813251,
%U 19487171,19902511,20796875,22665187,30080231,51064811,65450827,77854483,80062991,99252847
%N Perfect powers n such that (n-9)/2 is prime.
%C n must be an odd power of a number congruent to 3 modulo 4. - _Charlie Neder_, Feb 11 2019
%H Charlie Neder, <a href="/A075546/b075546.txt">Table of n, a(n) for n = 1..841</a>
%e a(1)=7^3, a(2)=11^3, a(3)=23^3, a(4)=31^3, a(5)=35^3, a(6)=43^3, a(7)=47^3, a(8)=67^3, a(9)=71^3, a(10)=95^3, a(11)=115^3, a(12)=131^3, a(13)=143^3, a(14)=23^5 and a(15)=211^3; most are cubes.
%t pp = Join[{1}, Select[ Range[10^7], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[(# - 9)/2] & ]
%K easy,nonn
%O 1,1
%A _Zak Seidov_, Oct 11 2002
%E Extended by _Robert G. Wilson v_, Oct 14 2002
%E a(16)=a(29) from _Charlie Neder_, Feb 11 2019
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