A009205 a(n) = gcd(d(n), sigma(n)).

1, 1, 2, 1, 2, 4, 2, 1, 1, 2, 2, 2, 2, 4, 4, 1, 2, 3, 2, 6, 4, 4, 2, 4, 1, 2, 4, 2, 2, 8, 2, 3, 4, 2, 4, 1, 2, 4, 4, 2, 2, 8, 2, 6, 6, 4, 2, 2, 3, 3, 4, 2, 2, 8, 4, 8, 4, 2, 2, 12, 2, 4, 2, 1, 4, 8, 2, 6, 4, 8, 2, 3, 2, 2, 2, 2, 4, 8, 2, 2, 1, 2, 2, 4, 4, 4, 4, 4, 2, 6, 4, 6, 4, 4, 4, 12, 2, 3, 6, 1, 2, 8, 2, 2, 8, 2, 2, 4, 2, 8, 4, 2, 2, 8, 4, 6, 2, 4, 4, 8

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A009191, A009194, A009278, A064840, A087801, A286360.

Programs

Mathematica

Table[GCD[DivisorSigma[0,n],DivisorSigma[1,n]],{n,120}] (* Harvey P. Dale, Dec 05 2017 *)

PARI

A009205(n) = gcd(numdiv(n),sigma(n)); \\ Antti Karttunen, May 22 2017

Python

from math import prod, gcd
from sympy import factorint
def A009205(n):
    f = factorint(n).items()
    return gcd(prod(e+1 for p, e in f),prod((p**(e+1)-1)//(p-1) for p,e in f)) # Chai Wah Wu, Jul 27 2023

Formula

a(n) = A064840(n)/A009278(n). - Amiram Eldar, Jan 31 2025

Extensions

Data section extended to 120 terms by Antti Karttunen, May 22 2017