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%I #17 Aug 24 2019 07:06:06
%S 8,25,32,121,2187,3125,32761,79507,97336,503284356
%N Perfect powers n with no primes between n and the next larger perfect power, which is in A116455.
%C No other n<10^12. There is a conjecture that this sequence is finite.
%C No other terms < 10^18. - _Jud McCranie_, Nov 03 2013
%C No other terms < 4.5*10^18. - _Giovanni Resta_, Apr 28 2014
%H <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A1=ind0603&L=nmbrthry">March 2006 NMBRTHRY Archives</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Redmond%E2%80%93Sun_conjecture">Redmond-Sun conjecture</a>
%e The prime-free ranges are (2^3,3^2), (5^2,3^3), (2^5,6^2), (11^2,5^3), (3^7,13^3), (5^5,56^2), (181^2,2^15), (43^3,282^2), (46^3,312^2), (22434^2,55^5).
%t lim=10^12; lst={}; k=2; While[n=Floor[lim^(1/k)]; n>=2, lst=Join[lst,Range[2,n]^k]; k++ ]; lst=Union[lst]; PrimeFree[n1_,n2_] := Module[{n=n1+1}, While[n<n2&&!PrimeQ[n], n++ ]; n ==n2]; lst2={}; Do[If[PrimeFree[lst[[i]],lst[[i+1]]], AppendTo[lst2,lst[[i]]]], {i,Length[lst]-1}]; lst2
%Y Cf. A001597 (perfect powers), A116455.
%Y Cf. A068435 (for prime powers).
%K hard,nonn
%O 1,1
%A _T. D. Noe_, Mar 28 2006
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