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%I #7 Jul 07 2019 20:20:33
%S 1,1,1,2,1,3,1,4,4,8,4,20,4,12,12,48,8,56,16,64,48,48,36,324,162,81,
%T 567,378,168,1680,168,1848,264,264,264,2640,240,288,288,3456,576,7488,
%U 1152,4032,4032,2016,1872,28080,9360,6240,3360,6720,3584,28672,6144
%N Number of maximal subsets of {1..n} containing n such that no two elements have the same sorted prime signature.
%C The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.
%F a(n) = A326439(n)/A064839(n).
%e The a(1) = 1 through a(12) = 20 subsets (A = 10, B = 11, C = 12) are the following. The common cardinality of sets in column n is A085089(n).
%e 1 12 13 124 145 1246 1467 12468 12689 1248A 1468B 12468C
%e 134 1346 13468 13689 1289A 148AB 1248AC
%e 1456 14568 15689 1348A 1689B 12689C
%e 14678 16789 1389A 189AB 1289AC
%e 1458A 13468C
%e 1478A 1348AC
%e 1589A 13689C
%e 1789A 1389AC
%e 14568C
%e 1458AC
%e 14678C
%e 1468BC
%e 1478AC
%e 148ABC
%e 15689C
%e 1589AC
%e 16789C
%e 1689BC
%e 1789AC
%e 189ABC
%t prisig[n_]:=If[n==1,{},Sort[Last/@FactorInteger[n]]];
%t Table[Times@@Length/@Split[Sort[Array[prisig,n]]]/Count[Array[prisig,n],prisig[n]],{n,30}]
%Y Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A324762, A325263, A325365, A326438, A326441.
%K nonn
%O 1,4
%A _Gus Wiseman_, Jul 06 2019
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