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

1,2

Comments

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

Links

Table of n, a(n) for n=1..75.

Example

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.

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 *)

Crossrefs

Cf. A000203, A008472, A099042.

Sequence in context: A153023 A068319 A133775 * A318677 A239327 A021047

Adjacent sequences: A099040 A099041 A099042 * A099044 A099045 A099046

Keyword

nonn

Author

Reinhard Zumkeller, Sep 23 2004

Status

approved