A178911 -id:A178911 - cp's OEIS frontend

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

Franklin T. Adams-Watters, Jun 22 2010

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.

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

Cf. A000203, A178908, A178911, A003987.

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

import Data.Bits (xor)
a178910 = foldl1 xor . a027750_row :: Integer -> Integer
-- Reinhard Zumkeller, Nov 17 2012

a(n)=local(ds,r);ds=divisors(n);for(k=1,#ds,r=bitxor(r,ds[k]));r

from sympy import divisors
def A178910(n):
    res = 1
    for divisor in divisors(n)[1:]: res ^= divisor
    return res # Karl-Heinz Hofmann, May 30 2025

A178909 Indices of perfect polynomials over GF(2).

Original entry on oeis.org

1, 6, 36, 54, 120, 2470, 2640, 3144, 3780, 32640, 41280, 52632, 67184, 1098176, 1157904, 2147450880

Offset: 1

Franklin T. Adams-Watters, Jun 22 2010

Numbers k such that k = A178908(k); sum of divisors of k-th GF(2) polynomial is the polynomial itself.

a(17) > 5*10^9. - Amiram Eldar, Oct 28 2019

Cf. A178908, A091220, A000396, A178911.

isok(n) = my(s = vecsum(divisors(Mod(1,2)*Pol(binary(n))))); subst(lift(s), x, 2) == n; \\ Michel Marcus, Jan 13 2019

a(14)-a(15) from Amiram Eldar, Jan 13 2019

a(16) from Amiram Eldar, Oct 28 2019

cp's OEIS Frontend

A178910 Binary XOR of divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

PARI

Python