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A328178 a(n) is the minimal value of the expression d XOR (n/d) where d runs through the divisors of n and XOR denotes the bitwise XOR operator.

%I A328178 #16 Nov 04 2019 14:52:34
%S A328178 0,3,2,0,4,1,6,6,0,7,10,4,12,5,6,0,16,5,18,1,4,9,22,2,0,15,10,3,28,3,
%T A328178 30,12,8,19,2,0,36,17,14,13,40,1,42,15,12,21,46,8,0,15,18,9,52,15,14,
%U A328178 10,16,31,58,9,60,29,14,0,8,13,66,21,20,11,70,1,72
%N A328178 a(n) is the minimal value of the expression d XOR (n/d) where d runs through the divisors of n and XOR denotes the bitwise XOR operator.
%H A328178 Rémy Sigrist, <a href="/A328178/b328178.txt">Table of n, a(n) for n = 1..16384</a>
%H A328178 Rémy Sigrist, <a href="/A328178/a328178.png">Logarithmic scatterplot of (n, 1+a(n)) for n = 1..2^16</a>
%F A328178 a(n) = 0 iff n is a square.
%F A328178 a(p) = p-1 for any odd prime number p.
%e A328178 For n = 12:
%e A328178 - we have the following values:
%e A328178     d   12/d  d XOR (12/d)
%e A328178     --  ----  ------------
%e A328178      1    12            13
%e A328178      2     6             4
%e A328178      3     4             7
%e A328178      4     3             7
%e A328178      6     2             4
%e A328178     12     1            13
%e A328178 - hence a(12) = min({4, 7, 13}) = 4.
%p A328178 a:= n-> min(seq(Bits[Xor](d, n/d), d=numtheory[divisors](n))):
%p A328178 seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 09 2019
%t A328178 mvx[n_]:=Min[BitXor[#,n/#]&/@Divisors[n]]; Array[mvx,80] (* _Harvey P. Dale_, Nov 04 2019 *)
%o A328178 (PARI) a(n) = vecmin(apply(d -> bitxor(d, n/d), divisors(n)))
%Y A328178 See A328176 and A328177 for similar sequences.
%Y A328178 Cf. A178910.
%K A328178 nonn,base
%O A328178 1,2
%A A328178 _Rémy Sigrist_, Oct 06 2019