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

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

Offset: 1

Author

Reinhard Zumkeller, Sep 23 2004

Keywords

• nonn

Comments

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

Examples

			a(24) = 2+3+8+12 = 25; A099042(24) = #{2,3,8,12} = 4;
a(25) = 5; A099042(25) = #{5} = 1;
a(26) = 2+13 = 15; A099042(26) = #{2,13} = 2.
		

Crossrefs

Cf. A000203, A008472, A099042.

Programs

Mathematica

b[1] = 0;
b[n_] := b[n] = Product[If[n > d^2, 1, 1 - b[d]], {d, Select[Range[n-1], Mod[n, #] == 0&]}];
a[n_] := Select[Divisors[n], b[#] == 1&] // Total;
Array[a, 100] (* Jean-François Alcover, Sep 18 2020 *)