A078710 Integer part of the subinterval variance in the partition of [0,n] by the divisors of n.

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, 60, 25, 364, 23, 420, 34, 93, 75, 166, 30, 612, 97, 133, 45, 760, 47, 840, 67, 124, 147, 1012, 50, 500, 93, 235, 96, 1300, 78, 410, 91, 297, 243, 1624, 69, 1740, 281, 254, 130, 576

Offset

2,4

Links

Table of n, a(n) for n=2..65.

Example

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.

Mathematica

<< 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}]

Crossrefs

Cf. A078709.

Sequence in context: A369905 A064279 A369908 * A175763 A080303 A145369

Adjacent sequences: A078707 A078708 A078709 * A078711 A078712 A078713

Keyword

nonn

Author

Joseph L. Pe, Dec 19 2002

Status

approved