A303481 Total volume of the family of rectangular prisms with dimensions p, q and p + q where p divides q, n = p + q and p < q.

0, 0, 6, 12, 20, 78, 42, 152, 234, 250, 110, 1080, 156, 518, 1500, 1456, 272, 2988, 342, 3880, 3612, 1342, 506, 10704, 3100, 1898, 7020, 9016, 812, 19050, 930, 12640, 12012, 3298, 13300, 37476, 1332, 4142, 18876, 39600, 1640, 45822, 1806, 28600, 51480, 6118

Offset: 1

Author

Wesley Ivan Hurt, Apr 24 2018

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A303385.

Programs

Mathematica

Table[Sum[n*i (n - i) (Floor[(n - i)/i] - Floor[(n - i - 1)/i]), {i, Floor[(n - 1)/2]}], {n, 50}]

Formula

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

a(n) = n * A303385(n).