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%I #16 Sep 02 2018 17:07:18
%S 0,1,-1,1,-1,0,-1,2,-3,0,-1,0,-1,0,-2,1,-1,-2,-1,0,-2,0,-1,1,-3,0,-4,
%T 0,-1,-1,-1,2,-2,0,-2,-2,-1,0,-2,1,-1,-1,-1,0,-4,0,-1,0,-3,-2,-2,0,-1,
%U -3,-2,1,-2,0,-1,-1,-1,0,-4,2,-2,-1,-1,0,-2,-1,-1,-1,-1,0,-4,0,-2,-1,-1,0,-7,0,-1,-1,-2,0,-2,1,-1,-3,-2,0
%N The 2-adic valuation of ratio A318649(n)/A318512(n); a(n) = 2*A007814(n) - A046645(n).
%C Also the 2-adic valuation of ratio A318681(n)/A299150(n) [which is equal to A318649(n)/A318512(n), but not represented in lowest terms], as well as the 2-adic valuation of A318680(n)/A299150(n) = A318511(n)/A318512(n).
%H Antti Karttunen, <a href="/A318656/b318656.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A318655(n) - A318513(n).
%F a(n) = A007814(n) - A318440(n).
%F a(n) = 2*A007814(n) - A046645(n) = A007814(n^2) - A046645(n).
%o (PARI)
%o A007814(n) = valuation(n,2);
%o A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A046644(n) = factorback(apply(e -> 2^A005187(e),factor(n)[,2]));
%o A318656(n) = ((2*A007814(n))-A007814(A046644(n)));
%Y Cf. A007814, A046645, A299150, A318440, A318511, A318512, A318513, A318649, A318655, A318680, A318681.
%Y Cf. A318654 (positions of positive terms).
%K sign
%O 1,8
%A _Antti Karttunen_, Sep 02 2018
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