A057021 Denominator of (sum of divisors of n / number of divisors of n).

1, 2, 1, 3, 1, 1, 1, 4, 3, 2, 1, 3, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 1, 2, 3, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 9, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 5, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 7, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Henry Bottomley, Jul 21 2000

Keywords

• frac
• nonn

Comments

a(n) = 1 when n is listed in A003601, a(n) > 1 when n is listed in A049642. - Alonso del Arte, Jan 31 2006

a(A069081(n)) = 2. - Bernard Schott, Sep 19 2019

Examples

			a(12)=3 since the 6 divisors of 12 are 1, 2, 3, 4, 6 and 12 and 1+2+3+4+6+12=28 and 28/6=14/3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A009205, A054025, A057020 (numerator), A057022, A069081.

Programs

Haskell

import Data.Ratio ((%), denominator)
a057021 n = denominator $ a000203 n % a000005 n
-- Reinhard Zumkeller, Jan 06 2012

Magma

[Denominator(SumOfDivisors(n)/#Divisors(n)):n in [1..100]]; // Marius A. Burtea, Sep 08 2019

Maple

with(numtheory): seq(denom(sigma(n)/tau(n)), n=1..70) ; # Zerinvary Lajos, Jun 04 2008

Mathematica

Denominator[Table[(Plus @@ Divisors[n])/Length[Divisors[n]], {n, 70}]] (* Alonso del Arte, Feb 24 2006 *)

PARI

a(n) = denominator(sigma(n)/numdiv(n)); \\ Michel Marcus, Apr 12 2016

SageMath

[denominator(sigma(n, 1)/sigma(n, 0)) for n in range(1, 71)] # Stefano Spezia, Jul 18 2025

Formula

a(n) = A057020(n)*A000005(n)/A000203(n) = A000005(n)/A009205(n).