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%I #14 Feb 16 2020 00:58:17
%S 15,26,35,143,215,323,511,899,1727,1763,2047,2186,2743,3599,5183,7999,
%T 10403,11663,13823,19043,22499,32399,36863,39203,51983,54871,57599,
%U 72899,79523,97343,121103,157463,176399,186623,213443,238327,248831,272483,279935,324899,359999,381923
%N Semiprimes which are sub-perfect powers.
%C Numbers of the form p*q where p and q are primes, not necessarily distinct, such that p*q + 1 is a perfect power (squares, cubes, etc.). In one sense, this is to semiprimes as Mersenne primes A000668 are to primes.
%C By Catalan's conjecture (or now Mihailescu's theorem), p and q are always distinct. - _T. D. Noe_, Apr 15 2011
%H T. D. Noe, <a href="/A189045/b189045.txt">Table of n, a(n) for n = 1..8433</a> (terms < 10^12)
%F A001358 INTERSECTION A045542. A001358 INTERSECTION {A001597 - 1}.
%e a(9) = 12^3 - 1 = 1727 = 11 * 157.
%t SemiPrimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; PerfectPowerQ[n_] := GCD @@ Last /@ FactorInteger[n] > 1; Select[Range[400000], SemiPrimeQ[#] && PerfectPowerQ[# + 1] &] (* _T. D. Noe_, Apr 15 2011 *)
%Y Cf. A001358, A001597, A045542, A177955, A189047.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Apr 15 2011
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