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A318515 a(n) = n AND A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.

%I A318515 #7 Aug 28 2018 15:59:00
%S A318515 1,0,1,0,1,2,1,0,1,0,1,4,1,6,5,0,1,0,1,0,5,2,1,8,1,8,9,12,1,14,1,0,1,
%T A318515 0,3,0,1,2,5,0,1,0,1,4,13,6,1,16,1,16,17,16,1,18,3,24,17,24,1,28,1,30,
%U A318515 21,0,1,0,1,0,5,2,1,0,1,0,9,4,9,6,1,0,17,0,1,0,17,2,21,8,1,8,9,12,29,14,19,32,1,32,33,32,1,34,1,32,33
%N A318515 a(n) = n AND A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.
%H A318515 Antti Karttunen, <a href="/A318515/b318515.txt">Table of n, a(n) for n = 1..65537</a>
%H A318515 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A318515 a(n) = A004198(n, A032742(n)).
%F A318515 a(n) = n + A032742(n) - A318514(n) = (n+A032742(n)-A106409(n))/2.
%o A318515 (PARI)
%o A318515 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A318515 A318515(n) = bitand(n,A032742(n));
%Y A318515 Cf. A004198, A032742, A060681, A106409, A318508, A318514, A318518.
%K A318515 nonn,base
%O A318515 1,6
%A A318515 _Antti Karttunen_, Aug 28 2018