Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Jun 28 2024 21:10:58
%S 1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,
%T 0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,1,1,1,1,0,0,
%U 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,0,1
%N a(n) = 1 if A328845(n) is a multiple of 3, otherwise 0, where A328845 is the first Fibonacci-based variant of the arithmetic derivative.
%H Antti Karttunen, <a href="/A374121/b374121.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(A328845(n)).
%o (PARI)
%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 A374121(n) = !(A328845(n)%3);
%Y Characteristic function of A374122.
%Y Cf. A079978, A328845.
%Y Cf. also A374045, A374051.
%K nonn
%O 0
%A _Antti Karttunen_, Jun 28 2024