A169811 -id:A169811 - 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

A070883 Bitwise XOR of n and n-th prime.

Original entry on oeis.org

3, 1, 6, 3, 14, 11, 22, 27, 30, 23, 20, 41, 36, 37, 32, 37, 42, 47, 80, 83, 92, 89, 68, 65, 120, 127, 124, 119, 112, 111, 96, 163, 168, 169, 182, 179, 184, 133, 128, 133, 154, 159, 148, 237, 232, 233, 252, 239, 210, 215, 218, 219, 196, 205, 310, 319, 308, 309, 302

Offset: 1

Reinhard Zumkeller, May 22 2002

For any integer k, XOR(n,k) = 2*OR(n,k) - (n+k). - Gary Detlefs, Oct 26 2013

			A000040(25)=97, [25]2 = '00011001', [97]2 = '01100001' '00011001' XOR '01100001' = '01111000', therefore a(25)=120.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, aut.
Eric Weisstein's World of Mathematics, XOR.

Cf. A169810, A169811, A194187.

Cf. A265885 (IMPL).

import Data.Bits (xor)
a070883 n = a070883_list !! (n-1)
a070883_list = zipWith xor [1..] a000040_list
-- Reinhard Zumkeller, Jun 23 2015

Table[ BitXor[ n, Prime[n]], {n, 1, 55}]

PARI
```
a(n) = bitxor(n, prime(n));
```

from sympy import prime
def a(n): return n^prime(n)
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Mar 05 2022

a(n) = 2*OR(p,n) - (p+n), for n-th prime p. - Gary Detlefs, Oct 26 2013

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

A169814 a(n) = n XOR phi(n).

Original entry on oeis.org

0, 3, 1, 6, 1, 4, 1, 12, 15, 14, 1, 8, 1, 8, 7, 24, 1, 20, 1, 28, 25, 28, 1, 16, 13, 22, 9, 16, 1, 22, 1, 48, 53, 50, 59, 40, 1, 52, 63, 56, 1, 38, 1, 56, 53, 56, 1, 32, 27, 38, 19, 44, 1, 36, 31, 32, 29, 38, 1, 44, 1, 32, 27, 96, 113, 86, 1, 100, 105, 94, 1, 80, 1, 110, 99, 104, 113, 86

Offset: 1

N. J. A. Sloane, May 28 2010

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

Cf. A000010, A065091, A070883, A169810, A169811, A169812, A169813.

a:= n-> Bits[Xor](n, numtheory[phi](n)):
seq(a(n), n=1..89);  # Alois P. Heinz, Jul 06 2023

Table[BitXor[n,EulerPhi[n]],{n,80}] (* Harvey P. Dale, Sep 18 2011 *)

a(n)=bitxor(n,eulerphi(n)) \\ Charles R Greathouse IV, Feb 21 2013

a(n) = 1 <=> n in { A065091 }. - Alois P. Heinz, Jul 06 2023

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

A070883 Bitwise XOR of n and n-th prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Python

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Scheme

A169814 a(n) = n XOR phi(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI