cp's OEIS Frontend

A178910 Binary XOR of divisors of n.

%I A178910 #17 May 30 2025 11:01:31
%S A178910 1,3,2,7,4,6,6,15,11,12,10,14,12,10,8,31,16,29,18,28,16,30,22,30,29,
%T A178910 20,16,18,28,24,30,63,40,48,32,49,36,54,40,60,40,48,42,54,44,58,46,62,
%U A178910 55,39,32,36,52,48,56,34,40,36,58,56,60,34,38,127,72,120,66,112,80,96,70
%N A178910 Binary XOR of divisors of n.
%C A178910 If 2^k <= n < 2^(k+1), then also 2^k <= a(n) < 2^(k+1), since any proper divisor of n is < 2^k.
%H A178910 Reinhard Zumkeller, <a href="/A178910/b178910.txt">Table of n, a(n) for n = 1..8191</a>
%o A178910 (PARI) a(n)=local(ds,r);ds=divisors(n);for(k=1,#ds,r=bitxor(r,ds[k]));r
%o A178910 (Haskell)
%o A178910 import Data.Bits (xor)
%o A178910 a178910 = foldl1 xor . a027750_row :: Integer -> Integer
%o A178910 -- _Reinhard Zumkeller_, Nov 17 2012
%o A178910 (Python)
%o A178910 from sympy import divisors
%o A178910 def A178910(n):
%o A178910     res = 1
%o A178910     for divisor in divisors(n)[1:]: res ^= divisor
%o A178910     return res # _Karl-Heinz Hofmann_, May 30 2025
%Y A178910 Cf. A000203, A178908, A178911, A003987.
%Y A178910 Cf. A027750, A072594; subsequences A028982 (odd), A028982 (even).
%K A178910 base,nonn,look
%O A178910 1,2
%A A178910 _Franklin T. Adams-Watters_, Jun 22 2010