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%I #10 Aug 30 2019 13:12:13
%S 1,1,1,2,2,3,3,4,4,8,16,20,20,24,36,48,48,56,112,128,192,240,288,324,
%T 324,486,567,1134,1512,1680,1680,1848,1848,2112,2376,2640,2640,2880,
%U 3168,3456,6912,7488,14976,16128,20160,24192,26208,28080,28080,37440,43680
%N Number of maximal subsets of {1..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.
%H Andrew Howroyd, <a href="/A326439/b326439.txt">Table of n, a(n) for n = 0..1000</a>
%e The a(0) = 1 through a(9) = 8 subsets:
%e {} {1} {12} {12} {124} {124} {1246} {1246} {12468} {12468}
%e {13} {134} {134} {1346} {1346} {13468} {12689}
%e {145} {1456} {1456} {14568} {13468}
%e {1467} {14678} {13689}
%e {14568}
%e {14678}
%e {15689}
%e {16789}
%t prisig[n_]:=If[n==1,{},Sort[Last/@FactorInteger[n]]];
%t Table[Times@@(Length/@Split[Sort[Array[prisig,n]]]),{n,0,30}]
%o (PARI) a(n)={if(n==0, 1, my(M=Map()); for(i=1, n, my(f=factor(i)[,2], s=sum(k=1, #f, x^f[k]), z); mapput(M, s, if(mapisdefined(M, s, &z), z + 1, 1))); vecprod(Mat(M)[,2]))} \\ _Andrew Howroyd_, Aug 30 2019
%Y Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A324762, A325263, A325365, A326438, A326441.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jul 06 2019
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