A303479 Total volume of the family of rectangular prisms with dimensions p, q, and |q - p| where p divides q, n = p + q and p < q.

0, 0, 2, 6, 12, 36, 30, 90, 110, 168, 90, 560, 132, 396, 756, 930, 240, 1692, 306, 2436, 1876, 1140, 462, 6120, 2052, 1656, 3620, 5928, 756, 11304, 870, 8370, 6084, 2976, 8988, 22070, 1260, 3780, 9364, 26220, 1560, 27720, 1722, 18912, 29304, 5676, 2070

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

Formula

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