A178910 Binary XOR of divisors of n.

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, 20, 16, 18, 28, 24, 30, 63, 40, 48, 32, 49, 36, 54, 40, 60, 40, 48, 42, 54, 44, 58, 46, 62, 55, 39, 32, 36, 52, 48, 56, 34, 40, 36, 58, 56, 60, 34, 38, 127, 72, 120, 66, 112, 80, 96, 70

Offset

1,2

Comments

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.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..8191

Prog

(PARI) a(n)=local(ds, r); ds=divisors(n); for(k=1, #ds, r=bitxor(r, ds[k])); r
(Haskell)
import Data.Bits (xor)
a178910 = foldl1 xor . a027750_row :: Integer -> Integer
-- Reinhard Zumkeller, Nov 17 2012

Crossrefs

Cf. A000203, A178908, A178911, A003987.

Cf. A027750, A072594; subsequences A028982 (odd), A028982 (even).

Sequence in context: A371974 A344878 A344875 * A182651 A175055 A351207

Adjacent sequences: A178907 A178908 A178909 * A178911 A178912 A178913

Keyword

base,nonn,look

Author

Franklin T. Adams-Watters, Jun 22 2010

Status

approved