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%I #11 May 26 2017 04:31:28
%S 1,1,1,4,1,4,1,10,4,4,1,16,1,4,4,30,1,16,1,16,4,4,1,54,4,4,10,16,1,22,
%T 1,75,4,4,4,74,1,4,4,54,1,22,1,16,16,4,1,176,4,16,4,16,1,54,4,54,4,4,
%U 1,102,1,4,16,206,4,22,1,16,4,22,1,267,1,4,16,16,4,22,1,176,30,4,1,102
%N Number of ways of factoring n with 2 levels of parentheses.
%C a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
%H R. J. Mathar, <a href="/A050338/b050338.txt">Table of n, a(n) for n = 1..1679</a>
%F Dirichlet g.f.: Product_{n>=2}(1/(1-1/n^s)^A050336(n)).
%F a(n) = A050339(A101296(n)). - _R. J. Mathar_, May 26 2017
%e 4 = ((4)) = ((2*2)) = ((2)*(2)) = ((2))*((2)).
%Y Cf. A001055, A050336-A050341. a(p^k)=A007713. a(A002110)=A000307.
%K nonn
%O 1,4
%A _Christian G. Bower_, Oct 15 1999
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