%I
%S 0,0,4,9,6,15,12,0,9,18,20,27,12,18,33,12,30,27,0,36,45,30,18,51,44,
%T 36,45,54,36,63,24,40,45,60,66,27,54,60,68,81,54,87,60,0,66,81,90,84,
%U 75,36,105,60,102,72,99,72,36,117,90,90,123,108,108,81,88,126,116,135,102,48
%N Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2 and the 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 pmax2 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin+1. If the product of this modified list of factors, k*(pmax2)*(pmin+1)/(pmin*pmax), is nonprime, it is added to the sequence.
%e k(1)=(p(max)=2)*(p(min)=2), transformed (22)*(2+1)=0*3=0=a(1).
%e k(2)=(p(max)=3)*(p(min)=2), transformed (32)*(2+1)=1*3=3 (prime, skipped).
%e k(3)=(p(max)=2)*(p=2)*(p(min)=2), transformed (22)*2*(2+1)=0*2*3=0=a(2), etc.
%Y Cf. A141218, A141219, A141220, A141284.
%K nonn
%O 1,3
%A _JuriStepan Gerasimov_, Aug 14 2008
%E Edited and corrected by _R. J. Mathar_, Aug 18 2008
