%I #9 Sep 18 2020 06:04:41

%S 0,2,3,2,5,5,7,10,3,7,11,17,13,9,8,10,17,23,19,7,10,13,23,25,5,15,30,

%T 9,29,40,31,10,14,19,12,35,37,21,16,15,41,12,43,13,53,25,47,25,7,57,

%U 20,15,53,50,16,17,22,31,59,52,61,33,73,10,18,16,67,19,26,84,71,43,73,39,83

%N Sum of badly sieved (A066680) divisors of n.

%C A008472(n) <= a(n) <= A000203.

%e a(24) = 2+3+8+12 = 25; A099042(24) = #{2,3,8,12} = 4;

%e a(25) = 5; A099042(25) = #{5} = 1;

%e a(26) = 2+13 = 15; A099042(26) = #{2,13} = 2.

%t b[1] = 0;

%t b[n_] := b[n] = Product[If[n > d^2, 1, 1 - b[d]], {d, Select[Range[n-1], Mod[n, #] == 0&]}];

%t a[n_] := Select[Divisors[n], b[#] == 1&] // Total;

%t Array[a, 100] (* _Jean-François Alcover_, Sep 18 2020 *)

%Y Cf. A000203, A008472, A099042.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Sep 23 2004