%I A141466
%S A141466 1,4,4,4,6,8,4,6,8,12,10,8,16,12,12,12,12,8,20,16,24,12,18,24,16,18,20,
               24,
%T A141466 22,16,36,20,32,24,18,40,24,36,28,24,30,36,16,48,30,32,44,30,24,36,40,
               36,
%U A141466 60,36,32,36,40,36,64,42,56,40,36,72,44,60,46,72,32,42,60,40,48,48,60,
               52
%N A141466 Nonprime transformed products of prime factors of the composites, the 
               largest and smallest prime decremented by 1.
%C A141466 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. If the product of this modified set of factors, k*(pmax-1)*(pmin-1)/
               (pmin*pmax), is nonprime, it is added to the sequence.
%e A141466 If k(1)=4=(p(max)=2)*(p(min)=2), then (2-1)*(2-1)=1*1=1=a(1).
%e A141466 If k(2)=6=(p(max)=3)*(p(min)=2), then (3-1)*(2-1)=2*1=2 (prime).
%e A141466 If k(3)=8=(p(max)=2)*(p=2)*(p(min)=2), then (2-1)*2*(2-1)=1*2*1=2 (prime).
%e A141466 If k(4)=9=(p(max)=3)*(p(min)=3), then (3-1)*(3-1)=2*2=4=a(2).
%e A141466 If k(5)=10=(p(max)=5)*(p(min)=2), then (5-1)*(2-1)=4*1=4=a(3).
%e A141466 If k(6)=12=(p(max)=3)*(p=2)*(p(min)=2), then (3-1)*2*(2-1)=2*2*1=4=a(4).
%e A141466 If k(7)=14=(p(max)=7)*(p(min)=2), then (7-1)*(2-1)=6*1=6=a(5).
%e A141466 If k(8)=15=(p(max)=5)*(p(min)=3), then (5-1)*(3-1)=4*2=8=a(6),
%e A141466 If k(9)=16=(p(max)=2)*2*2*(p(min)=2), then (2-1)*2*2*(2-1)=1*2*2*1=4=a(7).
%e A141466 If k(10)=18=(p(max)=3)*(p=3)*(p(min)=2), then (3-1)*3*(2-1)=2*3*1=6=a(8), 
               etc.
%Y A141466 Sequence in context: A073229 A102126 A097918 this_sequence A023958 A137751 
               A010658
%Y A141466 Adjacent sequences: A141463 A141464 A141465 this_sequence A141467 A141468 
               A141469
%K A141466 nonn
%O A141466 1,2
%A A141466 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru) Aug 08 2008
%E A141466 Definition rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 14 2008