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A325263 Number of subsets of {1..n} containing n such that no two elements have the same sorted prime signature.

%I A325263 #7 Jul 07 2019 20:20:25
%S A325263 1,2,2,6,4,16,8,40,40,60,36,216,72,168,168,840,240,960,360,1080,864,
%T A325263 864,672,6720,4480,2560,10240,7680,3840,42240,7680,92160,23040,23040,
%U A325263 23040,253440,42240,49920,49920,324480,74880,524160,112320,336960,336960,181440
%N A325263 Number of subsets of {1..n} containing n such that no two elements have the same sorted prime signature.
%C A325263 The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.
%F A325263 a(n) = A326438(n)/(1 + A064839(n)).
%e A325263 The a(1) = 1 through a(5) = 16 subsets:
%e A325263   {1}  {2}    {3}    {4}      {5}      {6}        {7}
%e A325263        {1,2}  {1,3}  {1,4}    {1,5}    {1,6}      {1,7}
%e A325263                      {2,4}    {4,5}    {2,6}      {4,7}
%e A325263                      {3,4}    {1,4,5}  {3,6}      {6,7}
%e A325263                      {1,2,4}           {4,6}      {1,4,7}
%e A325263                      {1,3,4}           {5,6}      {1,6,7}
%e A325263                                        {1,2,6}    {4,6,7}
%e A325263                                        {1,3,6}    {1,4,6,7}
%e A325263                                        {1,4,6}
%e A325263                                        {1,5,6}
%e A325263                                        {2,4,6}
%e A325263                                        {3,4,6}
%e A325263                                        {4,5,6}
%e A325263                                        {1,2,4,6}
%e A325263                                        {1,3,4,6}
%e A325263                                        {1,4,5,6}
%t A325263 prisig[n_]:=If[n==1,{},Sort[Last/@FactorInteger[n]]];
%t A325263 Table[Times@@(1+Length/@Split[Sort[Array[prisig,n]]])/(1+Count[Array[prisig,n],prisig[n]]),{n,30}]
%Y A325263 Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A325365, A326438, A326439, A326441.
%K A325263 nonn
%O A325263 1,2
%A A325263 _Gus Wiseman_, Jul 06 2019