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A338528 Number of partitions of k*n into two parts (s,t) such that s <= t and t | k*s for k = 1..n.

%I A338528 #14 Feb 01 2021 20:20:52
%S A338528 0,2,2,5,4,11,7,13,11,19,11,27,15,28,30,34,20,45,23,52,46,49,28,71,45,
%T A338528 58,54,78,37,105,42,81,77,79,85,124,51,90,91,137,57,156,61,134,143,
%U A338528 115,67,178,102,160,128,162,75,187,150,206,144,143,84,276,91,156,213,199,181,263
%N A338528 Number of partitions of k*n into two parts (s,t) such that s <= t and t | k*s for k = 1..n.
%H A338528 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A338528 a(n) = Sum_{k=1..n} Sum_{i=1..floor(n*k/2)} (1 - ceiling(k*i/(k*n-i)) + floor(k*i/(k*n-i))).
%e A338528 a(6) = 11; The 11 partitions of 6*1, 6*2, ..., 6*6 into 2 parts (s,t) such that s <= t and t | k*s for k = 1..n are:
%e A338528 6: (3,3),
%e A338528 12: (4,8), (6,6),
%e A338528 18: (9,9),
%e A338528 24: (8,16), (12,12),
%e A338528 30: (5,25), (15,15),
%e A338528 36: (9,24), (12,24), (18,18).
%t A338528 Table[Sum[Sum[(1 - Ceiling[k*i/(k*n - i)] + Floor[k*i/(k*n - i)]), {i, Floor[k*n/2]}], {k, n}], {n, 50}]
%Y A338528 Cf. A338021.
%K A338528 nonn
%O A338528 1,2
%A A338528 _Wesley Ivan Hurt_, Nov 07 2020