|
%I #8 Jul 15 2019 01:44:10
%S 0,1,2,3,6,7,8,9,12,19,20,21,28,29,30,31,40,41,70,71,74,75,76,77,108,
%T 123,124,211,214,215,216,217,332,333,334,335,592,593,594,595,612,613,
%U 614,615,618,639,640,641,1160,1183,1324,1325,1328,1329,2176,2177,2196
%N Number of subsets of {1..n} whose geometric mean is an integer.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric mean</a>
%e The a(1) = 1 through a(9) = 19 subsets:
%e {1} {1} {1} {1} {1} {1} {1} {1} {1}
%e {2} {2} {2} {2} {2} {2} {2} {2}
%e {3} {3} {3} {3} {3} {3} {3}
%e {4} {4} {4} {4} {4} {4}
%e {1,4} {5} {5} {5} {5} {5}
%e {1,2,4} {1,4} {6} {6} {6} {6}
%e {1,2,4} {1,4} {7} {7} {7}
%e {1,2,4} {1,4} {8} {8}
%e {1,2,4} {1,4} {9}
%e {2,8} {1,4}
%e {1,2,4} {1,9}
%e {2,4,8} {2,8}
%e {4,9}
%e {1,2,4}
%e {1,3,9}
%e {2,4,8}
%e {3,8,9}
%e {4,6,9}
%e {3,6,8,9}
%t Table[Length[Select[Subsets[Range[n]],IntegerQ[GeometricMean[#]]&]],{n,0,10}]
%Y First differences are A082553.
%Y Partitions whose geometric mean is an integer are A067539.
%Y Strict partitions whose geometric mean is an integer are A326625.
%Y Subsets whose average is an integer are A051293.
%Y Cf. A078174, A078175, A102627, A326567/A326568, A326622, A326623, A326624.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jul 14 2019
|
