OFFSET
1,2
FORMULA
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))).
EXAMPLE
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:
6: (3,3),
12: (4,8), (6,6),
18: (9,9),
24: (8,16), (12,12),
30: (5,25), (15,15),
36: (9,24), (12,24), (18,18).
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 07 2020
STATUS
approved