A373256 - OEIS

%I #9 Jun 01 2024 08:14:52

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

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

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

%N a(n) = 1 if A003415(n) == -1 (mod 3), otherwise 0, where A003415 is the arithmetic derivative.

%C Question: Do the asymptotic means of this sequence, A373254 and A359430 all converge to 1/3, or do they differ or diverge?

%H Antti Karttunen, <a href="/A373256/b373256.txt">Table of n, a(n) for n = 0..100000</a>

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

%F a(n) = [A373253(n) == -1], where [ ] is the Iverson bracket.

%F a(n) = 1 - (A359430(n)+A373254(n)).

%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 A373256(n) = (2==(A003415(n)%3));

%Y Characteristic function of A373257.

%Y Cf. A003415, A359430, A373253, A373254.

%K nonn

%O 0

%A _Antti Karttunen_, Jun 01 2024