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%I #10 Sep 03 2022 21:28:39
%S 1,1,1,5,1,5,1,15,5,5,1,25,1,5,5,55,1,25,1,25,5,5,1,105,5,5,15,25,1,
%T 35,1,170,5,5,5,145,1,5,5,105,1,35,1,25,25,5,1,425,5,25,5,25,1,105,5,
%U 105,5,5,1,205,1,5,25,571,5,35,1,25,5,35,1,660,1,5,25,25,5,35,1,425,55,5
%N Number of ways of factoring n with 3 levels of parentheses.
%C a(n) depends only on the 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="/A050340/b050340.txt">Table of n, a(n) for n = 1..1295</a>
%F Dirichlet g.f.: Product{n=2..infinity} (1/(1-1/n^s)^A050338(n)).
%F a(n) = A050341(A101296(n)). - _R. J. Mathar_, May 26 2017
%e 4 = (((4))) = (((2*2))) = (((2)*(2))) = (((2))*((2))) = (((2)))*(((2))).
%Y Cf. A001055, A050336-A050341. a(p^k) = A007714. a(A002110) = A000357.
%K nonn
%O 1,4
%A _Christian G. Bower_, Oct 15 1999
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