A318456 a(n) = n OR A001065(n), where OR is bitwise-or (A003986) and A001065 = sum of proper divisors.

1, 3, 3, 7, 5, 6, 7, 15, 13, 10, 11, 28, 13, 14, 15, 31, 17, 23, 19, 22, 31, 30, 23, 60, 31, 26, 31, 28, 29, 62, 31, 63, 47, 54, 47, 55, 37, 54, 55, 58, 41, 62, 43, 44, 45, 62, 47, 124, 57, 59, 55, 62, 53, 118, 55, 120, 63, 58, 59, 124, 61, 62, 63, 127, 83, 78, 67, 126, 95, 78, 71, 123, 73, 106, 123, 76, 95, 94, 79, 122, 121, 126, 83

Offset: 1

Author

Antti Karttunen, Aug 26 2018

Keywords

• nonn
• base

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)

Crossrefs

Cf. A000203, A001065, A003986, A318457, A318458, A318466.

Programs

Mathematica

Array[BitOr[#, DivisorSigma[1, #] - #] &, 100] (* Paolo Xausa, Mar 11 2024 *)

PARI

A318456(n) = bitor(n,sigma(n)-n);

Python

from sympy import divisor_sigma
def A318456(n): return n|divisor_sigma(n)-n # Chai Wah Wu, Jul 01 2022

Formula

a(n) = A003986(n, A001065(n)).

a(n) = A000203(n) - A318458(n).