%I #23 Sep 08 2022 08:46:22

%S 0,0,1,0,1,6,1,0,0,8,1,0,1,10,9,0,1,16,1,20,1,6,1,0,0,16,9,28,1,10,1,

%T 0,1,0,1,36,1,6,1,32,1,34,1,40,33,10,1,0,0,34,17,36,1,2,17,0,17,32,1,

%U 44,1,34,41,0,1,66,1,0,1,66,1,72,1,8,1,64,1,74,1,64,0,0,1,4,21,6,1,88,1,16,17,76,1,18,25,0,1,64,33,100,1,98,1,104,65

%N a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors.

%C The peculiar look of the scatterplot is partly an artifact of the logarithmic scale. Compare also to the scatterplot of A318468.

%H Antti Karttunen, <a href="/A318458/b318458.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>

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

%F a(n) = A004198(n, A001065(n)).

%F a(n) = A000203(n) - A318456(n) = (A000203(n)-A318457(n))/2.

%t Table[BitAnd[n, DivisorSigma[1, n] - n], {n, 100}] (* _Vincenzo Librandi_, Aug 29 2018 *)

%o (PARI) A318458(n) = bitand(n,sigma(n)-n);

%o (Magma) [SumOfDivisors(n)-BitwiseOr(n, SumOfDivisors(n)-n): n in [1..100]]; // _Vincenzo Librandi_, Aug 29 2018

%Y Cf. A000203, A001065, A004198, A033879, A318456, A318457.

%Y Cf. also A318468, A318508, A318518, A318463.

%K nonn,base,look

%O 1,6

%A _Antti Karttunen_, Aug 26 2018