A334349 Total area of all r X s rectangles with integer side lengths such that r + s = n, r < s and (s - r) | (s * r).

0, 0, 2, 0, 6, 8, 12, 12, 38, 24, 30, 32, 42, 48, 196, 108, 72, 152, 90, 96, 406, 120, 132, 456, 306, 168, 524, 192, 210, 784, 240, 684, 1036, 288, 1050, 608, 342, 360, 1456, 1416, 420, 1624, 462, 480, 3120, 528, 552, 3188, 1188, 1224, 2506, 672, 702, 2096, 2832

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Formula

a(n) = Sum_{i=1..floor((n-1)/2)} i * (n-i) * (1 - ceiling(i*(n-i)/(n-2*i)) + floor(i*(n-i)/(n-2*i))).

Example

a(9) = 38; 9 has two rectangles, 3 X 6 and 4 X 5, such that (6 - 3) | (6 * 3) = 3 | 18 and (5 - 4) | (5 * 4) = 1 | 20. The sum of the areas is then 3*6 + 4*5 = 18 + 20 = 38.

Mathematica

Table[Sum[i (n - i) (1 - Ceiling[i (n - i)/(n - 2 i)] + Floor[i (n - i)/(n - 2 i)]), {i, Floor[(n - 1)/2]}], {n, 80}]

Crossrefs

Sequence in context: A087996 A086777 A355978 * A058498 A358167 A348189

Adjacent sequences: A334346 A334347 A334348 * A334350 A334351 A334352

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 24 2020

Status

approved