cp's OEIS Frontend

A227320 Binary XOR of proper divisors of n.

%I A227320 #22 Oct 09 2017 00:05:15
%S A227320 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 A227320 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 A227320 30,1,4,1,28,25,63,9,58,1,52,21,38,1,33,1,38,17,50,13,54,1
%N A227320 Binary XOR of proper divisors of n.
%C A227320 An alternative definition (with A027751) would define a(1)=1. - _R. J. Mathar_, Jul 14 2013
%C A227320 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 A227320 Antti Karttunen, <a href="/A227320/b227320.txt">Table of n, a(n) for n = 1..16383</a>
%F A227320 a(n) = A178910(n) XOR n, where XOR is the binary logical exclusive or operator.
%F A227320 From _Antti Karttunen_, Oct 08 2017: (Start)
%F A227320 a(n) = A248663(A293214(n)).
%F A227320 a(n) <= A218403(n) <= A001065(n).
%F A227320 (End)
%t A227320 Array[BitXor @@ Most@ Divisors@ # &, 79] (* _Michael De Vlieger_, Oct 08 2017 *)
%o A227320 (PARI) A227320(n) = { my(s=0); fordiv(n,d,if(d<n,s = bitxor(s,d))); s; }; \\ _Antti Karttunen_, Oct 08 2017
%Y A227320 Cf. A001065, A027751, A178910, A218403, A248663, A293214, A293215.
%K A227320 nonn,base,look
%O A227320 1,4
%A A227320 _Alex Ratushnyak_, Jul 06 2013