A374117 - OEIS

%I #7 Jul 08 2024 16:41:00

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

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

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

%N a(n) = 1 if A328768(n) and A328845(n) are both multiples of 3, otherwise 0, where A328768 is the first primorial based variant and A328845 is the first Fibonacci-based variant of the arithmetic derivative, respectively.

%H Antti Karttunen, <a href="/A374117/b374117.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) = A079978(A374116(n)).

%F a(n) = A373991(n) * A374121(n).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/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 A374117(n) = (!(A328768(n)%3) && !(A328845(n)%3));

%Y Characteristic function of A374118.

%Y Cf. A079978, A328768, A328845, A373991, A374121, A374116.

%K nonn

%O 0

%A _Antti Karttunen_, Jul 08 2024