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A318457 a(n) = n XOR A001065(n), where XOR is bitwise-xor (A003987) and A001065 = sum of proper divisors.

%I A318457 #11 Dec 16 2024 16:14:11
%S A318457 1,3,2,7,4,0,6,15,13,2,10,28,12,4,6,31,16,7,18,2,30,24,22,60,31,10,22,
%T A318457 0,28,52,30,63,46,54,46,19,36,48,54,26,40,28,42,4,12,52,46,124,57,25,
%U A318457 38,26,52,116,38,120,46,26,58,80,60,28,22,127,82,12,66,126,94,12,70,51,72,98,122,12,94,20,78,58,121,126,82,216,66
%N A318457 a(n) = n XOR A001065(n), where XOR is bitwise-xor (A003987) and A001065 = sum of proper divisors.
%H A318457 Antti Karttunen, <a href="/A318457/b318457.txt">Table of n, a(n) for n = 1..65537</a>
%H A318457 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A318457 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A318457 a(n) = A003987(n, A001065(n)).
%F A318457 a(n) = A000203(n) - 2*A318458(n).
%t A318457 Array[BitXor[#, DivisorSigma[1, #] - #] &, 100] (* _Paolo Xausa_, Dec 16 2024 *)
%o A318457 (PARI) A318457(n) = bitxor(n,sigma(n)-n);
%Y A318457 Cf. A000203, A001065, A003987, A033879, A318456, A318458, A318467.
%Y A318457 Cf. A000396 (positions of zeros).
%K A318457 nonn,base
%O A318457 1,2
%A A318457 _Antti Karttunen_, Aug 26 2018