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

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

1,2

Comments

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.

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A088203 A205649 A176510 * A342464 A061342 A104639

Adjacent sequences: A362948 A362949 A362950 * A362952 A362953 A362954

Keyword

nonn,base,less

Author

Darío Clavijo, Jul 05 2023

Status

approved