|
%I #2 Feb 11 2014 19:05:33
%S 0,0,0,4,1,12,2,7,3,40,4,60,9,17,8,112,9,144,13,35,27,220,14,104,41,
%T 60,25,364,23,420,34,93,75,166,30,612,97,133,45,760,47,840,67,124,147,
%U 1012,50,500,93,235,96,1300,78,410,91,297,243,1624,69,1740,281,254,130,576
%N Integer part of the subinterval variance in the partition of [0,n] by the divisors of n.
%e The divisors of 9 partition the closed interval [0,9] into subintervals [0,1), [1,3), [3,9], with lengths 1, 2, 6, respectively. The variance of these lengths has integer part = 3. Hence a(9) = 3.
%t << Statistics`DescriptiveStatistics` f[n_] := Module[{d, l, a, i}, d = Divisors[n]; l = Length[d]; a = {1}; For[i = 1, i <= l - 1, i++, a = Append[a, d[[i + 1]] - d[[i]]]]; a]; Table[Floor[Variance[f[i]]], {i, 2, 100}]
%Y Cf. A078709.
%K nonn
%O 2,4
%A _Joseph L. Pe_, Dec 19 2002
|
