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A326438 Number of subsets of {1..n} such that no two elements have the same sorted prime signature.

%I A326438 #8 Jul 07 2019 20:20:40
%S A326438 1,2,4,6,12,16,32,40,80,120,180,216,432,504,672,840,1680,1920,2880,
%T A326438 3240,4320,5184,6048,6720,13440,17920,20480,30720,38400,42240,84480,
%U A326438 92160,184320,207360,230400,253440,506880,549120,599040,648960,973440
%N A326438 Number of subsets of {1..n} such that no two elements have the same sorted prime signature.
%C A326438 The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.
%e A326438 The a(0) = 1 through a(5) = 16 subsets:
%e A326438   {}  {}   {}     {}     {}       {}
%e A326438       {1}  {1}    {1}    {1}      {1}
%e A326438            {2}    {2}    {2}      {2}
%e A326438            {1,2}  {3}    {3}      {3}
%e A326438                   {1,2}  {4}      {4}
%e A326438                   {1,3}  {1,2}    {5}
%e A326438                          {1,3}    {1,2}
%e A326438                          {1,4}    {1,3}
%e A326438                          {2,4}    {1,4}
%e A326438                          {3,4}    {1,5}
%e A326438                          {1,2,4}  {2,4}
%e A326438                          {1,3,4}  {3,4}
%e A326438                                   {4,5}
%e A326438                                   {1,2,4}
%e A326438                                   {1,3,4}
%e A326438                                   {1,4,5}
%t A326438 prisig[n_]:=If[n==1,{},Sort[Last/@FactorInteger[n]]];
%t A326438 Table[Length[Select[Subsets[Range[n]],UnsameQ@@prisig/@#&]],{n,0,10}]
%Y A326438 Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A325263, A325365, A326439, A326441.
%K A326438 nonn
%O A326438 0,2
%A A326438 _Gus Wiseman_, Jul 06 2019