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%I #25 Jan 02 2023 12:30:50
%S 8,45,125,343,325,833,1331,1573,2197,2057,3211,3289,4913,4901,6859,
%T 6647,8303,10051,10469,11191,12167,15341,16399,17081,18259,22103,
%U 24389,26071,29791,27347,31117,35557,36163,36859,39401,42439,50653,50933,52111,56129,56699
%N Maximal non-semiprime number which is a "preprime" of the n-th kind (defined in comment in A247395).
%C Conjecture: the sequence contains all cubes of primes, except for 3^3 (cf. A030078).
%C Prime(n)^3 is in the sequence iff the interval [prime(n)^(3/2), prime(n)*sqrt(prime(n+1))] contains a prime.
%C A simple algorithm for finding the position k=k(n) for which a(k) = prime(n)^3 is given in A247835 (see formula and example there).
%C Conjecture: every term has the form a(n)= p*q*r, where p<=q<=r are primes.
%H Vladimir Shevelev , <a href="http://list.seqfan.eu/oldermail/seqfan/2014-September/013643.html">A classification of the positive integers over primes</a>
%Y Cf. A030078, A156759, A247393, A247394, A247395, A247396, A247509, A247510, A247511, A247606, A247835, A247867.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Sep 24 2014
%E More terms from _Peter J. C. Moses_, Sep 24 2014
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