%I A088434
%S A088434 0,0,0,0,0,1,0,1,0,1,0,2,0,1,1,1,0,2,0,2,1,1,0,4,0,1,1,2,0,4,0,2,1,1,1,
%T A088434 4,0,1,1,4,0,4,0,2,2,1,0,6,0,2,1,2,0,4,1,4,1,1,0,8,0,1,2,3,1,4,0,2,1,4,
%U A088434 0,8,0,1,2,2,1,4,0,6,1,1,0,8,1,1,1,4,0,8,1,2,1,1,1,9,0,2,2,4,0,4
%N A088434 Number of ways to write n as n = u*v*w with 1<=u<v<w.
%C A088434 a(n)=0 iff n=1 or n prime or n prime^2: a(A000430(n))=0.
%C A088434 The integers a(n)+1 equal A045778(n) for n<120 and differ at all n that 
               admit factorization into 4 or more distinct factors, the smallest 
               ones being n=120=2*3*4*5, n=144=2*3*4*6, n=168=2*3*4*7, n=180=2*3*5*6, 
               ..., later continueing n=312=2*3*4*13, n=320=2*4*5*8, n=324=2*3*6*9, 
               n=330=2*3*5*11,... Coincidentally, A068350(5) to A068350(19) start 
               this list. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 19 
               2007
%e A088434 n=12: (1,2,6), (1,3,4): therefore a(12)=2;
%e A088434 n=18: (1,2,9), (1,3,6): therefore a(18)=2.
%Y A088434 Cf. A034836, A088432, A088433.
%Y A088434 Sequence in context: A084114 A110475 A086971 this_sequence A034178 A131341 
               A074169
%Y A088434 Adjacent sequences: A088431 A088432 A088433 this_sequence A088435 A088436 
               A088437
%K A088434 nonn
%O A088434 1,12
%A A088434 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 01 2003