A297024 Sum of the smaller parts of the partitions of n into two parts such that the smaller part does not divide the larger.

0, 0, 0, 0, 2, 0, 5, 3, 6, 7, 14, 5, 20, 18, 19, 21, 35, 24, 44, 33, 44, 52, 65, 42, 72, 75, 78, 77, 104, 78, 119, 105, 121, 133, 140, 116, 170, 168, 173, 160, 209, 177, 230, 213, 220, 250, 275, 224, 292, 282, 304, 305, 350, 312, 361, 342, 383, 403, 434, 357

Offset: 1

Author

Wesley Ivan Hurt, Dec 23 2017

Keywords

• nonn
• easy

Examples

			a(10) = 7; the partitions of 10 into two parts are (9,1), (8,2), (7,3), (6,4), (5,5). The sum of the smaller parts that do not divide their larger counterparts is then 3 + 4 = 7.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to partitions

Crossrefs

Cf. A296955.

Programs

GAP

List(List(List([1..10^2], n-> Partitions(n,2)), i -> Filtered(i, j -> j[1] mod j[2] <> 0)), m->Sum(m, k -> k[2])); # Muniru A Asiru, Jan 28 2018

Mathematica

Table[Sum[i (1 - (Floor[n/i] - Floor[(n - 1)/i])), {i, Floor[n/2]}], {n, 100}]
f[n_] := Plus @@ Select[ Range[n/2], !MemberQ[Divisors[n], #] &]; Array[f, 60] (* Robert G. Wilson v, Dec 23 2017 *)
Table[Total[Select[IntegerPartitions[n,{2}],Mod[#[[1]],#[[2]]]!=0&][[All,2]]],{n,60}] (* Harvey P. Dale, Dec 17 2021 *)

Formula

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