A334289 - OEIS

%I #17 Feb 01 2021 21:38:34

%S 0,0,4,6,6,8,8,22,22,12,12,68,14,16,78,62,18,44,20,104,104,24,24,234,

%T 56,28,94,140,30,156,32,158,156,36,178,326,38,40,182,372,42,208,44,

%U 212,400,48,48,638,106,112,234,248,54,188,262,496,260,60,60,1040

%N Sum of the lengths of all r X s rectangles such that r < s, r + s = 2n and (s - r) | (s * r).

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

%e a(8) = 22; 2*8 = 16 has two rectangles, 4 X 12 and 6 X 10, such that (12 - 4) | (12 * 4) = 8 | 48 and (10 - 6) | (10 * 6) = 4 | 60. The sum of the lengths of the rectangles is 12 + 10 = 22.

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

%Y Cf. A333754.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Apr 23 2020