A169814 -id:A169814 - cp's OEIS frontend

A169810 a(n) = n XOR n^2.

0, 0, 6, 10, 20, 28, 34, 54, 72, 88, 110, 114, 156, 164, 202, 238, 272, 304, 342, 378, 388, 428, 498, 518, 600, 616, 702, 706, 780, 852, 922, 990, 1056, 1120, 1190, 1258, 1332, 1404, 1410, 1494, 1640, 1720, 1742, 1810, 1980, 1988, 2154, 2190, 2352, 2384, 2550, 2586

Offset: 0

N. J. A. Sloane, May 28 2010

XOR the binary representations of n and n^2.

			a(5) = 28:
..101 <- 5
11001 <- 25
----- <- XOR
11100 -> 28

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Suggested by A174375. Cf. A070883, A169811-A169814.

Cf. A007745 (OR), A213541 (AND), A002378.

import Data.Bits (xor)
a169810 n = n ^ 2 `xor` n :: Integer
-- Reinhard Zumkeller, Dec 27 2012

f:=proc(n) local i,t0,t1,t2,ts,tl,n1,n2;
t1:=convert(n,base,2); t2:=convert(n^2,base,2); n1:=nops(t1); n2:=nops(t2);
if n1 < n2 then ts:= t1; tl:=t2; else ts:=t2; tl:=t1; fi;
t0:=[]; for i from 1 to nops(ts) do t0:=[op(t0), (ts[i] + tl[i]) mod 2 ]; od:
for i from nops(ts)+1 to nops(tl) do t0:=[op(t0), tl[i]]; od:
add(2^(i-1)*t0[i], i=1..nops(t0)); end;
# second Maple program:
a:= n-> Bits[Xor](n, n^2):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 29 2018

a[n_]:=BitXor[n, n^2]; Array[a, 60, 0] (* Robert G. Wilson v, Jun 09 2010 *)

A169810(n)=bitxor(n^2,n) \\ M. F. Hasler, May 07 2023

A169810=lambda n:n**2^n # M. F. Hasler, May 07 2023

A169813 a(n) = n XOR sigma(n), where sigma(n) is the number of divisors of n, A000203.

Original entry on oeis.org

0, 1, 7, 3, 3, 10, 15, 7, 4, 24, 7, 16, 3, 22, 23, 15, 3, 53, 7, 62, 53, 50, 15, 36, 6, 48, 51, 36, 3, 86, 63, 31, 17, 20, 19, 127, 3, 26, 31, 114, 3, 74, 7, 120, 99, 102, 31, 76, 8, 111, 123, 86, 3, 78, 127, 64, 105, 96, 7, 148, 3, 94, 87, 63, 21, 210, 7, 58, 37, 214, 15, 139, 3, 56

Offset: 1

N. J. A. Sloane, May 28 2010

Cf. A000203, A003987, A070883, A169810, A169811, A169812, A169814.

Cf. also A106409, A178910, A227320, A294899.

a(n) = bitxor(n, sigma(n)); \\ Michel Marcus, Nov 25 2017

(define (A169813 n) (A003987bi n (A000203 n))) ;; Where A003987bi implements the bitwise-XOR, A003987 and code for A000203 can be found under that entry. - Antti Karttunen, Nov 25 2017

A169812 a(n) = n XOR d(n) (cf. A000005).

Original entry on oeis.org

0, 0, 1, 7, 7, 2, 5, 12, 10, 14, 9, 10, 15, 10, 11, 21, 19, 20, 17, 18, 17, 18, 21, 16, 26, 30, 31, 26, 31, 22, 29, 38, 37, 38, 39, 45, 39, 34, 35, 32, 43, 34, 41, 42, 43, 42, 45, 58, 50, 52, 55, 50, 55, 62, 51, 48, 61, 62, 57, 48, 63, 58, 57, 71, 69, 74, 65, 66, 65, 78, 69, 68, 75, 78

Offset: 1

N. J. A. Sloane, May 28 2010

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A070883, A169810, A169811, A169813, A169814.

a[n_] := BitXor[n, DivisorSigma[0, n]]; Array[a, 100] (* Amiram Eldar, Jul 08 2019 *)

a(n)=bitxor(n, numdiv(n)); \\ Michel Marcus, Jul 08 2019

A362951 a(n) is the Hamming distance between the binary expansions of n and phi(n) where phi is the Euler totient function (A000010).

Original entry on oeis.org

0, 2, 1, 2, 1, 1, 1, 2, 4, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 3, 3, 3, 1, 1, 3, 3, 2, 1, 1, 3, 1, 2, 4, 3, 5, 2, 1, 3, 6, 3, 1, 3, 1, 3, 4, 3, 1, 1, 4, 3, 3, 3, 1, 2, 5, 1, 4, 3, 1, 3, 1, 1, 4, 2, 4, 4, 1, 3, 4, 5, 1, 2, 1, 5, 4, 3, 4, 4, 1, 3, 5, 5, 1, 3, 3, 5, 6

Offset: 1

Darío Clavijo, Jul 05 2023

a(2^k) = 2 for k >= 1.

a(p) = 1 for each odd prime p because phi(p) = p-1 and (p-1 xor p) = 1.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000010, A000120, A065091, A101080, A169814.

A362951[n_] := DigitCount[BitXor[n, EulerPhi[n]], 2, 1];
Array[A362951, 100] (* Paolo Xausa, Feb 20 2024 *)

from gmpy2 import mpz, hamdist
from sympy import totient
a = lambda n: hamdist(mpz(n), mpz(totient(n)))
print([a(n) for n in range(1, 87)])

from sympy import totient
def A362951(n): return (n^totient(n)).bit_count() # Chai Wah Wu, Jul 07 2023

a(n) = A101080(n,A000010(n)).

a(n) = A000120(A169814(n)).

cp's OEIS Frontend

A169810 a(n) = n XOR n^2.

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A169813 a(n) = n XOR sigma(n), where sigma(n) is the number of divisors of n, A000203.

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A169812 a(n) = n XOR d(n) (cf. A000005).

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A362951 a(n) is the Hamming distance between the binary expansions of n and phi(n) where phi is the Euler totient function (A000010).

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