A078713 Sum of squares of the distances between successive divisors of n.

0, 1, 4, 5, 16, 11, 36, 21, 40, 35, 100, 43, 144, 75, 108, 85, 256, 101, 324, 131, 216, 203, 484, 171, 416, 291, 364, 259, 784, 273, 900, 341, 552, 515, 804, 385, 1296, 651, 780, 519, 1600, 551, 1764, 659, 960, 971, 2116, 683, 1800, 885, 1356, 931, 2704, 911, 1988

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The divisors of 10 are 1, 2, 5, 10 and the sum of the squares of the distances between successive divisors = (2-1)^2 + (5-2)^2 + (10-5)^2 = 35. Hence a(10) = 35.

Mathematica

f[n_] := Module[{d, l, s, i}, d = Divisors[n]; l = Length[d]; s = 0; For[i = 1, i < l, i++, s = s + (d[[i + 1]] - d[[i]])^2]; s]; Table[f[n], {n, 1, 100}]
Table[Total[Differences[Divisors[n]]^2], {n, 60}] (* Harvey P. Dale, Apr 10 2018 *)

Crossrefs

Sequence in context: A244643 A085768 A166304 * A175263 A000695 A081345

Adjacent sequences: A078710 A078711 A078712 * A078714 A078715 A078716

Keyword

nonn

Author

Joseph L. Pe, Dec 19 2002

Status

approved