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A318455 The 2-adic valuation of A318454(n).

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%I A318455 #12 Sep 13 2018 02:42:11
%S A318455 0,1,0,3,0,1,0,4,0,1,0,3,0,1,0,7,0,1,0,3,0,1,0,4,0,1,0,3,0,1,0,8,0,1,
%T A318455 0,3,0,1,0,4,0,1,0,3,0,1,0,7,0,1,0,3,0,1,0,4,0,1,0,3,0,1,0,10,0,1,0,3,
%U A318455 0,1,0,4,0,1,0,3,0,1,0,7,0,1,0,3,0,1,0,4,0,1,0,3,0,1,0,8,0,1,0,3,0,1,0,4,0
%N A318455 The 2-adic valuation of A318454(n).
%H A318455 Antti Karttunen, <a href="/A318455/b318455.txt">Table of n, a(n) for n = 1..65537</a>
%F A318455 a(n) = A007814(A318454(n)).
%t A318455 f[1] = 1; f[n_] := f[n] = 1/2 (Sum[Mod[d, 2], {d, Divisors[n]}] - Sum[f[d] f[n/d], {d, Divisors[n][[2 ;; -2]]}]);
%t A318455 a[n_] := IntegerExponent[Denominator[f[n]], 2];
%t A318455 Array[a, 105] (* _Jean-François Alcover_, Sep 13 2018 *)
%o A318455 (PARI) A318455(n) = valuation(A318454(n),2); \\ Needs also program from A318454.
%Y A318455 Cf. A001227, A007814, A318453, A318454.
%Y A318455 Cf. also A046645, A317946, A318315, A318451.
%K A318455 nonn
%O A318455 1,4
%A A318455 _Antti Karttunen_ and _Andrew Howroyd_, Aug 29 2018