

A078710


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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: A019304 A072869 A064279 * A175763 A080303 A145369
Adjacent sequences: A078707 A078708 A078709 * A078711 A078712 A078713


KEYWORD

nonn


AUTHOR

Joseph L. Pe, Dec 19 2002


STATUS

approved



