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A099042
Number of badly sieved (A066680) divisors of n.
5
0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 3, 1, 2, 3, 2, 1, 4, 1, 3, 2, 2, 1, 4, 2, 3, 2, 2, 1, 5, 1, 2, 3, 2, 2, 3, 1, 2, 2, 4, 1, 5, 1, 2, 3, 2, 2, 3, 1, 4, 2, 2, 1, 4, 2, 2, 2, 3, 1, 6, 2, 2, 2, 2, 2, 4, 1, 3, 2, 3, 1, 3, 1, 3, 4
OFFSET
1,6
COMMENTS
A001221(n) <= a(n) <= A000005(n).
LINKS
FORMULA
a(n) = Sum_{d|n} A099104(d). - Antti Karttunen, Jul 02 2018
EXAMPLE
a(24) = #{2,3,8,12} = 4; A099043(24) = 2+3+8+12 = 25;
a(25) = #{5} = 1; A099043(25) = 5;
a(26) = #{2,13} = 2; A099043(26) = 2+13 = 15.
MATHEMATICA
b[n_] := b[n] = If[n == 1, 0, Product[If[n > d^2, 1, 1 - b[d]], {d, Select[Range[n - 1], Mod[n, #] == 0&]}]]; (* b is A099104 *)
a[n_] := Sum[b[d], {d, Divisors[n]}];
Array[a, 105] (* Jean-François Alcover, Dec 06 2021 *)
PROG
(PARI)
A099104(n) = if(1==n, 0, my(m=1); fordiv(n, d, if((d<n)&&((d*d)>=n), m *= (1-A099104(d)))); (m));
A099042(n) = sumdiv(n, d, A099104(d)); \\ Antti Karttunen, Jul 02 2018
CROSSREFS
Sequence in context: A325759 A292286 A341596 * A140774 A345345 A056924
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 23 2004
STATUS
approved