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

Author

Reinhard Zumkeller, Sep 26 2004

Keywords

• nonn

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

Crossrefs

Cf. A066680, A066682, A066683, A099042.

Programs

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 *)

PARI

A099104(n) = if(1==n,0,my(m=1); fordiv(n,d,if((d=n),m *= (1-A099104(d)))); (m)); \\ Antti Karttunen, Jul 02 2018

Formula

a(n) = Prod(if n>d^2 then 1 else 1-a(d): d

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