A099104 - OEIS

%I #16 Jul 02 2018 20:24:31

%S 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,

%T 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,

%U 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

%N Characteristic function of badly sieved numbers (A066680).

%C a(A066680(n)) = 1;

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

%H Antti Karttunen, <a href="/A099104/b099104.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%t 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 *)

%o (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

%Y Cf. A066680, A066682, A066683, A099042.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Sep 26 2004