A318463 - OEIS

%I #9 Jan 25 2024 12:35:19

%S 0,0,1,0,1,2,1,0,1,0,1,2,1,2,2,0,1,2,1,6,4,2,1,4,1,0,2,6,1,8,1,0,4,0,

%T 6,2,1,2,2,0,1,8,1,2,5,2,1,4,1,0,2,6,1,4,2,4,4,0,1,12,1,2,3,0,6,4,1,2,

%U 4,8,1,12,1,0,7,2,4,8,1,12,4,0,1,16,2,2,2,12,1,16,6,6,4,2,2,8,1,6,11,6,1,4,1,8,16

%N a(n) = Sum_{d|n, d < n/d} (d AND n/d), where AND is bitwise-and (A004198).

%H Antti Karttunen, <a href="/A318463/b318463.txt">Table of n, a(n) for n = 1..16384</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A000203(n) - A318461(n) = (A000203(n)-A318462(n))/2.

%o (PARI) A318463(n) = { my(ands=0); fordiv(n,d,if(d<(n/d), ands += bitand(d,n/d))); (ands); };

%Y Cf. A000203, A004198, A318458, A318460, A318461, A318462.

%K nonn,base

%O 1,6

%A _Antti Karttunen_, Aug 28 2018