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A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.

%I A318517 #7 Aug 28 2018 15:58:47
%S A318517 1,0,3,0,5,0,7,0,5,0,11,0,13,0,15,0,17,0,19,0,9,0,23,0,17,0,27,0,29,0,
%T A318517 31,0,29,0,27,0,37,0,23,0,41,0,43,0,17,0,47,0,45,0,51,0,53,0,39,0,53,
%U A318517 0,59,0,61,0,63,0,57,0,67,0,57,0,71,0,73,0,43,0,73,0,79,0,45,0,83,0,85,0,39,0,89,0,67,0,33,0,95
%N A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.
%H A318517 Antti Karttunen, <a href="/A318517/b318517.txt">Table of n, a(n) for n = 1..65537</a>
%H A318517 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A318517 a(n) = A003987(A032742(n), A060681(n)).
%F A318517 a(n) = n - 2*A318518(n).
%o A318517 (PARI)
%o A318517 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A318517 A318517(n) = bitxor(A032742(n),n-A032742(n));
%Y A318517 Cf. A003987, A032742, A060681, A106409, A318507, A318516, A318518.
%K A318517 nonn,base
%O A318517 1,3
%A A318517 _Antti Karttunen_, Aug 28 2018