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%I #6 Aug 28 2018 15:59:44
%S 0,1,1,2,1,6,1,4,5,8,1,20,1,10,9,8,1,22,1,28,11,14,1,48,7,16,9,20,1,
%T 44,1,16,15,20,13,52,1,22,17,32,1,48,1,36,45,26,1,96,9,36,21,60,1,94,
%U 17,88,23,32,1,76,1,34,39,32,19,72,1,44,27,68,1,120,1,40,63,84,19,92,1,80,37,44,1,184,23,46,33,112,1,132
%N Xor-Moebius transform of A001065, the sum of proper divisors.
%C Unique sequence satisfying SumXOR_{d divides n} a(d) = sigma(n)-n for all n > 0, where SumXOR is the analog of summation under the binary XOR operation. See A295901 for a list of some of the properties of Xor-Moebius transform.
%H Antti Karttunen, <a href="/A318503/b318503.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A318501(n) XOR A318502(n).
%o (PARI) A318503(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, sigma(d)-d))); (v); } \\ after code in A295901.
%Y Cf. A001065, A051953, A256739, A295901, A296203, A318501, A318502.
%K nonn
%O 1,4
%A _Antti Karttunen_, Aug 28 2018
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