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%I #4 Mar 30 2012 18:52:27
%S 9,12,18,16,18,24,24,24,36,36,36,32,36,48,36,42,48,48,54,72,48,54,48,
%T 72,60,56,72,72,72,72,72,96,64,90,72,84,108,72,96,80,90,108,96,96,144,
%U 84,108,108,96,120,144,114,120,120,96,126,144,144,126,144,108,132,120,144
%N Transformed products of prime factors of the composites, the largest prime and smallest prime incremented by 1.
%C In the prime number decomposition of k=A002808(i), i=1,2,3,.., one instance of the largest prime, pmax=A052369(i), is replaced by pmax+1 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin+1. The product of this modified list of factors, k*(pmax+1)*(pmin+1)/(pmin*pmax), is added to the sequence.
%e k(1)=4=(p(max)=2)*(p(min)=2), transformed (2+1)*(2+1)=3*3=9=a(1).
%e k(2)=6=(p(max)=3)*(p(min)=2), transformed (3+1)*(2+1)=4*3=12=a(2).
%e k(6)=12=(p(max)=3)*(p=2)*(p(min)=2), transformed (3+1)*2*(2+1)=4*2*3=24=a(6), etc.
%Y Cf. A141218, A141219, A141220, A141284.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 14 2008
%E Edited and corrected by _R. J. Mathar_, Aug 18 2008