cp's OEIS Frontend

A378227 XOR-Moebius transform of A318467, where A318467(n) = 2*n XOR sigma(n).

%I A378227 #10 Nov 26 2024 11:47:56
%S A378227 3,4,1,8,15,6,5,16,29,14,25,12,23,6,11,32,51,30,49,12,13,22,53,24,33,
%T A378227 14,1,12,39,126,29,64,105,70,127,20,111,70,99,24,123,58,121,12,15,38,
%U A378227 109,48,93,30,31,28,95,22,51,24,17,14,73,172,71,6,1,128,205,114,193,140,221,102,197,72,219,142,205,108
%N A378227 XOR-Moebius transform of A318467, where A318467(n) = 2*n XOR sigma(n).
%C A378227 Unique sequence satisfying SumXOR_{d divides n} a(d) = A318467(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 A378227 Antti Karttunen, <a href="/A378227/b378227.txt">Table of n, a(n) for n = 1..65537</a>
%H A378227 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A378227 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378227 a(n) = 2*A256739(n) XOR A296203(n).
%o A378227 (PARI)
%o A378227 A318467(n) = bitxor(2*n, sigma(n));
%o A378227 A378227(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318467(d)))); (v); }
%Y A378227 Cf. A000203, A003987, A256739, A296203, A318467.
%Y A378227 Cf. also A083254, A378226.
%K A378227 nonn
%O A378227 1,1
%A A378227 _Antti Karttunen_, Nov 26 2024