cp's OEIS Frontend

A378226 XOR-Moebius transform of A318457, where A318457(n) = n XOR (sigma(n)-n).

%I A378226 #10 Nov 26 2024 15:21:48
%S A378226 1,2,3,4,5,0,7,8,15,4,11,24,13,0,1,16,17,8,19,4,27,16,23,40,27,4,27,0,
%T A378226 29,52,31,32,39,36,45,8,37,32,57,16,41,0,43,24,5,32,47,80,63,0,53,20,
%U A378226 53,104,41,112,63,4,59,124,61,0,7,64,91,48,67,76,75,36,71,0,73,68,103,56,83,36,79,48,111,84,83
%N A378226 XOR-Moebius transform of A318457, where A318457(n) = n XOR (sigma(n)-n).
%C A378226 Unique sequence satisfying SumXOR_{d divides n} a(d) = A318457(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 A378226 Antti Karttunen, <a href="/A378226/b378226.txt">Table of n, a(n) for n = 1..65537</a>
%H A378226 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A378226 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A378226 (PARI)
%o A378226 A318457(n) = bitxor(n,sigma(n)-n);
%o A378226 A378226(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318457(d)))); (v); }
%Y A378226 Cf. A000203, A001065, A003987, A318457, A378227, A378230 (positions of 0's), A378441 (fixed points).
%K A378226 nonn
%O A378226 1,2
%A A378226 _Antti Karttunen_, Nov 26 2024