A078710 Integer part of the subinterval sample 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

Author

Joseph L. Pe, Dec 19 2002

Keywords

• nonn

Examples

			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 sample variance of these lengths has integer part = 7. Hence a(9) = 7. [Corrected by _Sean A. Irvine_, Jul 12 2025]
		

Crossrefs

Cf. A078709.

Programs

Mathematica

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}]