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

1,3

Links

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A121439 A307448 A305350 * A086754 A120880 A059151

Adjacent sequences: A009202 A009203 A009204 * A009206 A009207 A009208

Keyword

nonn

Author

David W. Wilson

Extensions

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

Status

approved