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

1,5

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A297024.

Sequence in context: A317825 A002346 A021327 * A167313 A104780 A176109

Adjacent sequences: A297050 A297051 A297052 * A297054 A297055 A297056

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 24 2017

Status

approved