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A331700 Binary XOR of squares of divisors of n. 1

%I #16 May 03 2023 16:15:54

%S 1,5,8,21,24,40,48,85,89,120,120,168,168,240,240,341,288,317,360,504,

%T 384,408,528,680,617,520,640,1008,840,816,960,1365,1072,1440,1248,

%U 1197,1368,1224,1360,2040,1680,1920,1848,1560,1864,2640,2208,2728,2385,3021

%N Binary XOR of squares of divisors of n.

%H Rémy Sigrist, <a href="/A331700/b331700.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A331700/a331700.png">Colored scatterplot of the first 2^18 terms</a> (where the color is function of A007814(n))

%e For n = 6:

%e - the divisors of 6 are 1, 2, 3 and 6,

%e - so a(6) = 1 XOR 4 XOR 9 XOR 36 = 40.

%t Table[BitXor@@(Divisors[n]^2),{n,50}] (* _Harvey P. Dale_, May 03 2023 *)

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

%o (Python)

%o from functools import reduce

%o from operator import xor

%o from sympy import divisors

%o def A331700(n): return reduce(xor,(d**2 for d in divisors(n,generator=True))) # _Chai Wah Wu_, Jul 01 2022

%Y Cf. A001157, A007814, A178910, A295901.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Jan 25 2020

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)