OFFSET
1,2
COMMENTS
Replacing "SumXOR" by "Sum" in the name leads to the Euler totient function (A000010).
Replacing "SumXOR" by "Product" in the name leads to the exponential of Mangoldt function (A014963).
a(p) = p-1 for any prime p>2.
a(2^k) = 2^k+2^(k-1) for any k>0.
The graph of this sequence is quite remarkable. - N. J. A. Sloane, Apr 09 2015
Xor-Moebius transform of natural numbers, A000027. See A295901 for a list of some of the properties of this transform. - Antti Karttunen, Dec 29 2017
LINKS
Paul Tek, Table of n, a(n) for n = 1..16383
Paul Tek, PARI program for this sequence
FORMULA
a(n) = n XOR ( SumXOR_{d divides n and d < n} a(d) ) for any n>0.
From Antti Karttunen, Dec 29 2017: (Start)
a(n) = SumXOR_{d|n} A296206(d).
(End)
MATHEMATICA
a = Table[0, {16383}];
Do[pa = n; Do[pa = BitXor[pa, a[[d]]], {d, Divisors[n]}]; a[[n]] = pa, {n, Length[a]}];
a (* Jean-François Alcover, Oct 18 2019, after Paul Tek *)
PROG
(PARI) See Links section.
A256739(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, d))); (v); } \\ Antti Karttunen, Dec 29 2017, after code in A295901.
CROSSREFS
KEYWORD
AUTHOR
Paul Tek, Apr 09 2015
STATUS
approved