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A318467 a(n) = 2*n XOR A000203(n), where XOR is bitwise-xor (A003987) and A000203 = sum of divisors.

%I A318467 #17 Jan 12 2025 10:16:32
%S A318467 3,7,2,15,12,0,6,31,31,6,26,4,20,4,6,63,48,3,50,2,10,8,54,12,45,30,30,
%T A318467 0,36,116,30,127,114,114,118,19,108,112,118,10,120,52,122,12,20,20,
%U A318467 110,28,91,57,46,10,92,20,38,8,34,46,74,208,68,28,22,255,214,20,194,246,234,28,198,83,216,230,234,20,250,52,206,26
%N A318467 a(n) = 2*n XOR A000203(n), where XOR is bitwise-xor (A003987) and A000203 = sum of divisors.
%H A318467 Antti Karttunen, <a href="/A318467/b318467.txt">Table of n, a(n) for n = 1..65537</a>
%H A318467 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A318467 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A318467 a(n) = A003987(2*n, A000203(n)).
%F A318467 a(n) = A224880(n) - 2*A318468(n).
%F A318467 a(n) = 2*n XOR (A318457(n)+2*A318458(n)). - _Antti Karttunen_, Jan 08 2025
%t A318467 Table[BitXor[2n,DivisorSigma[1,n]],{n,80}] (* _Harvey P. Dale_, Oct 30 2022 *)
%o A318467 (PARI) A318467(n) = bitxor(2*n,sigma(n));
%Y A318467 Cf. A000203, A003987, A318457, A318458, A318466, A318468.
%Y A318467 Cf. A000396 (positions of zeros), A378227 (XOR-Moebius transform), A379234 (fixed points), A379236.
%Y A318467 Cf. also A294899, A318457, A378988.
%K A318467 nonn,base
%O A318467 1,1
%A A318467 _Antti Karttunen_, Aug 26 2018