A355931 Greatest common divisor of the odd part of n and sigma(n), where sigma is the sum of divisors function.

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 3, 1, 1, 9, 7, 1, 1, 1, 5, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3

Offset: 1

Author

Antti Karttunen, Jul 22 2022

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000265, A009194, A161942.

Cf. also A355834.

Programs

Mathematica

a[n_] := GCD[DivisorSigma[1, n], n/2^IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Jul 22 2022 *)

PARI

A000265(n) = (n>>valuation(n,2));
A355931(n) = gcd(A000265(n), sigma(n));

Python

from math import gcd
from sympy import divisor_sigma
def A355931(n): return gcd(divisor_sigma(n),n>>(~n&n-1).bit_length()) # Chai Wah Wu, Jul 22 2022

Formula

a(n) = gcd(A000203(n), A000265(n)) = gcd(n, A161942(n)) = A000265(A009194(n)).