A373493 - OEIS

%I #6 Jun 10 2024 14:56:21

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

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

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

%N a(n) = 1 if A059975(n) and A003415(n) are both multiples of 3, otherwise 0, where A059975 is fully additive with a(p) = p-1, and A003415 is the arithmetic derivative.

%H Antti Karttunen, <a href="/A373493/b373493.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) = [A373378(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

%F a(n) >= A373491(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 A059975(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };

%o A373493(n) = (!(A059975(n)%3) && !(A003415(n)%3));

%Y Characteristic function of A373494.

%Y Cf. A003415, A059975, A373378, A373491.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 10 2024