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

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, 58, 54, 78, 37, 105, 42, 81, 77, 79, 85, 124, 51, 90, 91, 137, 57, 156, 61, 134, 143, 115, 67, 178, 102, 160, 128, 162, 75, 187, 150, 206, 144, 143, 84, 276, 91, 156, 213, 199, 181, 263

Offset: 1

Author

Wesley Ivan Hurt, Nov 07 2020

Keywords

• nonn

Examples

			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).
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A338021.

Programs

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}]

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))).