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A227320
Binary XOR of proper divisors of n.
7
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, 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, 30, 1, 4, 1, 28, 25, 63, 9, 58, 1, 52, 21, 38, 1, 33, 1, 38, 17, 50, 13, 54, 1
OFFSET
1,4
COMMENTS
An alternative definition (with A027751) would define a(1)=1. - R. J. Mathar, Jul 14 2013
However, this definition is more aligned with A001065 and A218403 where the initial term a(1) is also 0. - Antti Karttunen, Oct 08 2017
LINKS
FORMULA
a(n) = A178910(n) XOR n, where XOR is the binary logical exclusive or operator.
From Antti Karttunen, Oct 08 2017: (Start)
a(n) = A248663(A293214(n)).
a(n) <= A218403(n) <= A001065(n).
(End)
MATHEMATICA
Array[BitXor @@ Most@ Divisors@ # &, 79] (* Michael De Vlieger, Oct 08 2017 *)
PROG
(PARI) A227320(n) = { my(s=0); fordiv(n, d, if(d<n, s = bitxor(s, d))); s; }; \\ Antti Karttunen, Oct 08 2017
KEYWORD
nonn,base,look
AUTHOR
Alex Ratushnyak, Jul 06 2013
STATUS
approved