|
%I #8 Jul 07 2019 20:20:40
%S 1,2,4,6,12,16,32,40,80,120,180,216,432,504,672,840,1680,1920,2880,
%T 3240,4320,5184,6048,6720,13440,17920,20480,30720,38400,42240,84480,
%U 92160,184320,207360,230400,253440,506880,549120,599040,648960,973440
%N Number of 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.
%e The a(0) = 1 through a(5) = 16 subsets:
%e {} {} {} {} {} {}
%e {1} {1} {1} {1} {1}
%e {2} {2} {2} {2}
%e {1,2} {3} {3} {3}
%e {1,2} {4} {4}
%e {1,3} {1,2} {5}
%e {1,3} {1,2}
%e {1,4} {1,3}
%e {2,4} {1,4}
%e {3,4} {1,5}
%e {1,2,4} {2,4}
%e {1,3,4} {3,4}
%e {4,5}
%e {1,2,4}
%e {1,3,4}
%e {1,4,5}
%t prisig[n_]:=If[n==1,{},Sort[Last/@FactorInteger[n]]];
%t Table[Length[Select[Subsets[Range[n]],UnsameQ@@prisig/@#&]],{n,0,10}]
%Y Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A325263, A325365, A326439, A326441.
%K nonn
%O 0,2
%A _Gus Wiseman_, Jul 06 2019
|
