A331700 Binary XOR of squares of divisors of n.

1, 5, 8, 21, 24, 40, 48, 85, 89, 120, 120, 168, 168, 240, 240, 341, 288, 317, 360, 504, 384, 408, 528, 680, 617, 520, 640, 1008, 840, 816, 960, 1365, 1072, 1440, 1248, 1197, 1368, 1224, 1360, 2040, 1680, 1920, 1848, 1560, 1864, 2640, 2208, 2728, 2385, 3021

Offset: 1

Author

Rémy Sigrist, Jan 25 2020

Keywords

• nonn
• base

Examples

			For n = 6:
- the divisors of 6 are 1, 2, 3 and 6,
- so a(6) = 1 XOR 4 XOR 9 XOR 36 = 40.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, Colored scatterplot of the first 2^18 terms (where the color is function of A007814(n))

Crossrefs

Cf. A001157, A007814, A178910, A295901.

Programs

Mathematica

Table[BitXor@@(Divisors[n]^2),{n,50}] (* Harvey P. Dale, May 03 2023 *)

PARI

a(n) = my (s=0); fordiv (n, d, s=bitxor(s, d^2)); s

Python

from functools import reduce
from operator import xor
from sympy import divisors
def A331700(n): return reduce(xor,(d**2 for d in divisors(n,generator=True))) # Chai Wah Wu, Jul 01 2022