A374107 - OEIS

%I #7 Jun 29 2024 09:09:54

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

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

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

%N a(n) = 1 if A113177(n) and A328845(n) are both even, otherwise 0, where A113177 is fully additive with a(p) = Fibonacci(p) and A328845 is the first Fibonacci-based variant of the arithmetic derivative.

%H Antti Karttunen, <a href="/A374107/b374107.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) = A373585(n) * A374045(n).

%F a(n) = A059841(A374106(n)).

%o (PARI)

%o A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])));

%o A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])/f[i, 1]));

%o A374107(n) = (!(A113177(n)%2) && !(A328845(n)%2));

%Y Characteristic function of A374108.

%Y Cf. A059841, A113177, A328845, A373585, A374045, A374106.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 29 2024