%I #16 Dec 17 2021 18:46:30

%S 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,

%T 78,77,104,78,119,105,121,133,140,116,170,168,173,160,209,177,230,213,

%U 220,250,275,224,292,282,304,305,350,312,361,342,383,403,434,357

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

%H Muniru A Asiru, <a href="/A297024/b297024.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

%e 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.

%t Table[Sum[i (1 - (Floor[n/i] - Floor[(n - 1)/i])), {i, Floor[n/2]}], {n, 100}]

%t f[n_] := Plus @@ Select[ Range[n/2], !MemberQ[Divisors[n], #] &]; Array[f, 60] (* _Robert G. Wilson v_, Dec 23 2017 *)

%t Table[Total[Select[IntegerPartitions[n,{2}],Mod[#[[1]],#[[2]]]!=0&][[All,2]]],{n,60}] (* _Harvey P. Dale_, Dec 17 2021 *)

%o (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

%Y Cf. A296955.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Dec 23 2017