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%I #34 Jan 02 2023 12:30:50
%S 10,12,14,16,18,20,22,24,27,33,39,45,55,65,85,95,115,133,161,187,209,
%T 253,299,391,493,527,551,589,703,779,817,851,943,1073,1189,1247,1363,
%U 1457,1643,1739,1927,2173,2279,2537,2623,2867,3149,3337,3431,3551,3953
%N Numbers n such that the second maximal prime <= sqrt(n) is the least prime divisor of n.
%C These numbers we call "preprimes" of the second kind in contrast to A156759 for n>=2, for which the maximal prime <= sqrt(n) is the least prime divisor of n. Terms of A156759 (n>=2) we call "preprimes" (cf. comment there).
%H Jens Kruse Andersen, <a href="/A247393/b247393.txt">Table of n, a(n) for n = 1..10000</a>
%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-September/013643.html">A classification of the positive integers over primes</a>
%F lpf(a(n)) = prime(pi(sqrt(a(n))-1), where pi(n) = A000720(n).
%e a(1)=10. Indeed, in interval [2,sqrt(10)] we have two primes: 2 and 3. Maximal from them 3, the second maximal is 2, and 2=lpf(10).
%t Select[Range[4000], Prime[PrimePi[Sqrt[#]]-1] == FactorInteger[#][[1,1]] &] (* _Indranil Ghosh_, Mar 08 2017 *)
%o (PARI) select(n->prime(primepi(sqrtint(n))-1)==factor(n)[1, 1], vector(10^4, x, x+8)) \\ _Jens Kruse Andersen_, Sep 17 2014
%Y Cf. A156759.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Sep 16 2014
%E More terms from _Peter J. C. Moses_, Sep 16 2014
%E a(52..10000) from _Jens Kruse Andersen_, Sep 17 2014
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