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A099104 Characteristic function of badly sieved numbers (A066680). 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A073070 A189687 A284653 * A066829 A194664 A285975

Adjacent sequences:  A099101 A099102 A099103 * A099105 A099106 A099107

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 26 2004

STATUS

approved

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Last modified February 22 01:35 EST 2019. Contains 320381 sequences. (Running on oeis4.)