A297053 Sum of the larger parts of the partitions of n into two parts such that the smaller part does not divide the larger.

0, 0, 0, 0, 3, 0, 9, 5, 12, 13, 30, 7, 45, 38, 41, 43, 84, 48, 108, 67, 103, 124, 165, 78, 178, 185, 192, 175, 273, 162, 315, 247, 308, 343, 350, 244, 459, 440, 451, 360, 570, 411, 630, 535, 545, 670, 759, 496, 786, 718, 818, 787, 975, 768, 959, 834, 1042

Offset: 1

Author

Wesley Ivan Hurt, Dec 24 2017

Keywords

• nonn
• easy

Examples

			a(10) = 13; the partitions of 10 into two parts are (9,1), (8,2), (7,3), (6,4) and (5,5). The sum of the larger parts of these partitions such that the smaller part does not divide the larger is then 7 + 6 = 13.
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A297024.

Programs

Mathematica

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

Formula

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