A354807 - OEIS

%I #9 Jun 08 2022 15:48:56

%S 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,1,

%T 1,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,1,

%U 1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1

%N a(n) = 1 if A346241(n) is negative, and 0 otherwise, where A346241 is the Dirichlet inverse of {A003415, arithmetic derivative of n + A063524 (1, 0, 0, 0, ...)}.

%H Antti Karttunen, <a href="/A354807/b354807.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) = [A346241(n) < 0], where [ ] is the Iverson bracket

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o memoA346241 = Map();

%o A346241(n) = if(1==n,1,my(v); if(mapisdefined(memoA346241,n,&v), v, v = -sumdiv(n,d,if(d<n,A003415(n/d)*A346241(d),0)); mapput(memoA346241,n,v); (v)));

%o A354807(n) = (A346241(n)<0);

%Y Characteristic function of A354808, whose complement A354809 gives the positions of 0's.

%Y Cf. A003415, A346241, A354806.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 08 2022