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a(n) = 1 if A113177(n) is a multiple of 3, otherwise 0, where A113177 is fully additive with a(p) = Fibonacci(p).
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%I #7 Jun 28 2024 14:54:27

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

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

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

%N a(n) = 1 if A113177(n) is a multiple of 3, otherwise 0, where A113177 is fully additive with a(p) = Fibonacci(p).

%H Antti Karttunen, <a href="/A374051/b374051.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) = A079978(A113177(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 A374051(n) = !(A113177(n)%3);

%Y Characteristic function of A374052.

%Y Cf. A000045, A079978, A113177.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 28 2024