A387422 The length of the maximal common prefix of the binary expansions of n and sigma(n), where sigma is the sum of divisors function.

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

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to sigma(n).

Formula

a(n) = (1+A000523(n)) - A387423(n).

Mathematica

A387422[n_] := LengthWhile[Transpose[IntegerDigits[{n, DivisorSigma[1, n]}, 2][[All, ;; BitLength[n]]]], Equal @@ # &];
Array[A387422, 100] (* Paolo Xausa, Sep 03 2025 *)

Prog

(PARI) A387422(n) = { my(a=binary(n), b=binary(sigma(n)), i=1); while(i<=#a, if(a[i]!=b[i], return(i-1)); i++); (#a); };
(Python)
from os.path import commonprefix
from sympy import divisor_sigma
def A387422(n): return len(commonprefix([bin(n)[2:], bin(divisor_sigma(n))[2:]])) # Chai Wah Wu, Sep 03 2025

Crossrefs

Cf. A000203, A000523, A387423.

Cf. also A347380, A387412.

Sequence in context: A209155 A376369 A082062 * A030370 A100808 A010277

Adjacent sequences: A387419 A387420 A387421 * A387423 A387424 A387425

Keyword

nonn,base

Author

Antti Karttunen, Sep 01 2025

Status

approved