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A374206 The 2-adic valuation of A113177(n), where A113177 is fully additive with a(p) = Fibonacci(p).

%I A374206 #7 Jul 01 2024 15:27:00
%S A374206 0,1,1,0,0,0,0,2,1,0,2,0,1,0,2,0,0,0,0,0,1,0,0,1,1,1,0,0,3,0,0,0,1,1,
%T A374206 1,0,1,0,3,0,4,0,0,0,1,0,1,1,0,0,0,0,0,1,4,0,1,0,0,0,1,0,1,1,2,0,0,0,
%U A374206 0,0,0,0,1,2,0,1,2,0,0,3,1,0,0,1,1,0,2,0,1,1,0,0,1,1,0,0,0,0,2,0,6,0,2,2,1,0,3
%N A374206 The 2-adic valuation of A113177(n), where A113177 is fully additive with a(p) = Fibonacci(p).
%H A374206 Antti Karttunen, <a href="/A374206/b374206.txt">Table of n, a(n) for n = 2..100000</a>
%F A374206 a(n) = A007814(A113177(n)).
%o A374206 (PARI)
%o A374206 A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])));
%o A374206 A374206(n) = valuation(A113177(n), 2);
%Y A374206 Cf. A007814, A113177, A373586 (gives the indices of nonzero terms here, after its initial 1), A373587 (gives the indices of 0's).
%Y A374206 Cf. also A374132, A374212, A374202, A374207, A374208.
%K A374206 nonn
%O A374206 2,8
%A A374206 _Antti Karttunen_, Jul 01 2024