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

1,4

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

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

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

Crossrefs

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

Sequence in context: A151512 A106800 A308484 * A318507 A055807 A364285

Adjacent sequences: A227317 A227318 A227319 * A227321 A227322 A227323

Keyword

nonn,base,look

Author

Alex Ratushnyak, Jul 06 2013

Status

approved