A227320 Binary XOR of proper divisors of n.

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

Author

Alex Ratushnyak, Jul 06 2013

Keywords

• nonn
• base
• look

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

• Antti Karttunen, Table of n, a(n) for n = 1..16383

Crossrefs

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

Programs

Mathematica

Array[BitXor @@ Most@ Divisors@ # &, 79] (* Michael De Vlieger, Oct 08 2017 *)

PARI

A227320(n) = { my(s=0); fordiv(n,d,if(dAntti Karttunen, Oct 08 2017

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)