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%I #16 Oct 03 2018 03:38:55
%S 1,1,1,2,1,5,1,5,2,5,1,13,1,5,5,9,1,13,1,13,5,5,1,62,2,5,5,13,1,59,1,
%T 16,5,5,5,90,1,5,5,62,1,59,1,13,13,5,1,192,2,13,5,13,1,62,5,62,5,5,1,
%U 817,1,5,13,32,5,59,1,13,5,59,1,885,1,5,13,13,5,59,1,192,9,5,1,817,5,5
%N Each c(i) is "multiply" (*) or "divide" (/); d(1) = 1 < d(2) < ... < d(m) = n are the divisors of n; a(n) is number of choices for c(1), ..., c(m-1) so that d(1) c(1) d(2) c(2) d(3), .., c(m-1) d(m) is an integer.
%C a(n) = number of partitions of the set of divisors of n into two subsets U and V such that min(U) < min(V) and product(V) divides product(U). [_Reinhard Zumkeller_, Apr 05 2012]
%C It would appear that a(n) depends only on n's prime signature. - _Charlie Neder_, Oct 02 2018
%H Reinhard Zumkeller, <a href="/A060448/b060448.txt">Table of n, a(n) for n = 1..1000</a>
%H Reinhard Zumkeller, <a href="/A060448/a060448.lhs.txt">Example for n = 120</a>
%F a(A008578(n)) = 1; a(A002808(n)) > 1. [_Reinhard Zumkeller_, Apr 05 2012]
%e For n = 6 there are 5 possibilities: 1*2*3*6=36, 1/2*3*6=9, 1*2/3*6=4, 1/2/3*6=1, 1*2*3/6=1 For n = 18 there are 13 possibilities: 1*2*3*6*9*18 1/2*3*6*9*18 1*2/3*6*9*18 1*2*3/6*9*18 1*2*3*6/9*18 1*2*3*6*9/18 1/2/3*6*9*18 1/2/3*6/9*18 1/2*3*6/9*18 1*2/3/6*9*18 1*2/3*6/9*18 1*2/3*6*9/18 1*2*3/6/9*18
%o (Haskell)
%o import Data.List (subsequences, (\\))
%o a060448 n = length [us | let ds = a027750_row n,
%o us <- init $ tail $ subsequences ds,
%o let vs = ds \\ us, head us < head vs,
%o product us `mod` product vs == 0] + 1
%o -- _Reinhard Zumkeller_, Apr 05 2012
%Y Cf. A058524, A060636.
%K nonn,nice
%O 1,4
%A _Naohiro Nomoto_, Apr 14 2001
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