%I
%S 1,2,4,3,4,8,4,4,9,8,4,12,4,8,16,5,4,18,4,12,16,8,4,16,9,8,16,12,4,32,
%T 4,6,16,8,16,27,4,8,16,16,4,32,4,12,36,8,4,20,9,18,16,12,4,32,16,16,
%U 16,8,4,48,4,8,36,7,16,32,4,12,16,32,4,36,4,8,36,12,16,32,4,20
%N Number of distinct rectangles that can be made with one even and one odd side length that are divisors of 2n.
%C If p > 2 is prime, a(p) = 4. There are 4 rectangles that can be made with one even and one odd side length that are divisors of 2p: 1 X 2, 1 X 2p, 2 X p, and p X 2p.  _Wesley Ivan Hurt_, May 21 2021
%F a(n) = Sum_{d1(2*n), d2(2*n), d1<d2} (1  [d1 mod 2 = d2 mod 2]), where [ ] is the Iverson bracket.
%e a(6) = 8; The divisors of 2*6 = 12 are {1,2,3,4,6,12}. There are 8 distinct rectangles with one odd and one even side length using these divisors. They are 1 X 2, 1 X 4, 1 X 6, 1 X 12, 2 X 3, 3 X 4, 3 X 6, and 3 X 12.
%t Table[Sum[Sum[KroneckerDelta[Mod[i + 1, 2], Mod[k, 2]]*(1  Ceiling[2n/k] + Floor[2n/k]) (1  Ceiling[2n/i] + Floor[2n/i]), {i, k1}], {k, 2n}], {n, 100}]
%Y Cf. A337532.
%K nonn,easy
%O 1,2
%A _Wesley Ivan Hurt_, Sep 13 2020
