A373383 - OEIS

%I #6 Jun 06 2024 09:47:51

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

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

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

%N a(n) = 1 if n and A059975(n) are both multiples of 3, otherwise 0, where A059975 is fully additive with a(p) = p-1.

%C Question: What is the asymptotic mean of this sequence?

%H Antti Karttunen, <a href="/A373383/b373383.txt">Table of n, a(n) for n = 1..100000</a>

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

%F a(n) = [A373368(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

%o (PARI)

%o A059975(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };

%o A373383(n) = !(gcd(n, A059975(n))%3);

%Y Characteristic function of A373384.

%Y Cf. A059975, A373368.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 06 2024