A303479 - OEIS

%I #10 Nov 25 2024 05:00:28

%S 0,0,2,6,12,36,30,90,110,168,90,560,132,396,756,930,240,1692,306,2436,

%T 1876,1140,462,6120,2052,1656,3620,5928,756,11304,870,8370,6084,2976,

%U 8988,22070,1260,3780,9364,26220,1560,27720,1722,18912,29304,5676,2070

%N 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.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

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

%Y Cf. A303385.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Apr 24 2018