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A114331 Observe that A052248(n) = greatest prime divisor q (say) of all composite numbers between p = prime(n) and next prime. There is only one composite number in this range which is divisible by q. Sequence lists these composite numbers.

%I A114331 #15 Feb 16 2025 08:32:59
%S A114331 4,6,10,12,14,18,22,26,30,34,38,42,46,51,58,60,62,69,72,74,82,86,94,
%T A114331 99,102,106,108,111,122,129,134,138,146,150,155,158,166,172,178,180,
%U A114331 183,192,194,198,206,218,226,228,232,237,240,249,254,262,267,270
%N A114331 Observe that A052248(n) = greatest prime divisor q (say) of all composite numbers between p = prime(n) and next prime. There is only one composite number in this range which is divisible by q. Sequence lists these composite numbers.
%C A114331 The uniqueness follows from generalization of Bertrand's Postulate. - _Franklin T. Adams-Watters_.
%H A114331 Robert Israel, <a href="/A114331/b114331.txt">Table of n, a(n) for n = 2..10000</a>
%H A114331 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate</a>
%p A114331 p:= 3: R:= NULL:
%p A114331 for i from 2 to 100 do
%p A114331   pp:= p; p:= nextprime(p);
%p A114331   rmax:= 0:
%p A114331   for q from pp+1 to p-1 do
%p A114331     r:= max(numtheory:-factorset(q));
%p A114331     if r > rmax then rmax:= r; qmax:= q fi
%p A114331   od;
%p A114331   R:= R, qmax
%p A114331 od:
%p A114331 R; # _Robert Israel_, Apr 01 2021
%Y A114331 Cf. A052248, A114349.
%K A114331 nonn
%O A114331 2,1
%A A114331 _N. J. A. Sloane_, based on correspondence from _Leroy Quet_ and _Hugo Pfoertner_, Feb 22 2006