A099104 Characteristic function of badly sieved numbers (A066680).

0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1

Offset

1,1

Comments

a(A066680(n)) = 1;

A066683(n)=Sum(a(k):1<=k<=n); A066682(n)=a(n)*A066683(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = Prod(if n>d^2 then 1 else 1-a(d): d<n and n mod d = 0); a(1)=0.

Mathematica

a[1] = 0; a[n_] := a[n] = Product[ If[ n > d^2, 1, 1-a[d]], {d, Select[ Range[n-1], Mod[n, #] == 0 &] } ]; Table[ a[n], {n, 1, 105}](* Jean-François Alcover, Feb 15 2012, after formula *)

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)); \\ Antti Karttunen, Jul 02 2018

Crossrefs

Cf. A066680, A066682, A066683, A099042.

Sequence in context: A353817 A284653 A359158 * A358769 A066829 A194664

Adjacent sequences: A099101 A099102 A099103 * A099105 A099106 A099107

Keyword

nonn

Author

Reinhard Zumkeller, Sep 26 2004

Status

approved