A318515 - OEIS

%I #7 Aug 28 2018 15:59:00

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

%H Antti Karttunen, <a href="/A318515/b318515.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A004198(n, A032742(n)).

%F a(n) = n + A032742(n) - A318514(n) = (n+A032742(n)-A106409(n))/2.

%o (PARI)

%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A318515(n) = bitand(n,A032742(n));

%Y Cf. A004198, A032742, A060681, A106409, A318508, A318514, A318518.

%K nonn,base

%O 1,6

%A _Antti Karttunen_, Aug 28 2018