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Binary XOR of proper divisors of n.
7

%I #22 Oct 09 2017 00:05:15

%S 0,1,1,3,1,0,1,7,2,6,1,2,1,4,7,15,1,15,1,8,5,8,1,6,4,14,11,14,1,6,1,

%T 31,9,18,3,21,1,16,15,20,1,26,1,26,1,20,1,14,6,21,19,16,1,6,15,26,17,

%U 30,1,4,1,28,25,63,9,58,1,52,21,38,1,33,1,38,17,50,13,54,1

%N Binary XOR of proper divisors of n.

%C An alternative definition (with A027751) would define a(1)=1. - _R. J. Mathar_, Jul 14 2013

%C However, this definition is more aligned with A001065 and A218403 where the initial term a(1) is also 0. - _Antti Karttunen_, Oct 08 2017

%H Antti Karttunen, <a href="/A227320/b227320.txt">Table of n, a(n) for n = 1..16383</a>

%F a(n) = A178910(n) XOR n, where XOR is the binary logical exclusive or operator.

%F From _Antti Karttunen_, Oct 08 2017: (Start)

%F a(n) = A248663(A293214(n)).

%F a(n) <= A218403(n) <= A001065(n).

%F (End)

%t Array[BitXor @@ Most@ Divisors@ # &, 79] (* _Michael De Vlieger_, Oct 08 2017 *)

%o (PARI) A227320(n) = { my(s=0); fordiv(n,d,if(d<n,s = bitxor(s,d))); s; }; \\ _Antti Karttunen_, Oct 08 2017

%Y Cf. A001065, A027751, A178910, A218403, A248663, A293214, A293215.

%K nonn,base,look

%O 1,4

%A _Alex Ratushnyak_, Jul 06 2013