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A099043 Sum of badly sieved (A066680) divisors of n.

%I A099043 #9 Sep 18 2020 06:04:41
%S A099043 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 A099043 9,29,40,31,10,14,19,12,35,37,21,16,15,41,12,43,13,53,25,47,25,7,57,
%U A099043 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 A099043 Sum of badly sieved (A066680) divisors of n.
%C A099043 A008472(n) <= a(n) <= A000203.
%e A099043 a(24) = 2+3+8+12 = 25; A099042(24) = #{2,3,8,12} = 4;
%e A099043 a(25) = 5; A099042(25) = #{5} = 1;
%e A099043 a(26) = 2+13 = 15; A099042(26) = #{2,13} = 2.
%t A099043 b[1] = 0;
%t A099043 b[n_] := b[n] = Product[If[n > d^2, 1, 1 - b[d]], {d, Select[Range[n-1], Mod[n, #] == 0&]}];
%t A099043 a[n_] := Select[Divisors[n], b[#] == 1&] // Total;
%t A099043 Array[a, 100] (* _Jean-François Alcover_, Sep 18 2020 *)
%Y A099043 Cf. A000203, A008472, A099042.
%K A099043 nonn
%O A099043 1,2
%A A099043 _Reinhard Zumkeller_, Sep 23 2004