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

1,2

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(Haskell)
import Data.Ratio ((%), denominator)
a057021 n = denominator $ a000203 n % a000005 n
-- Reinhard Zumkeller, Jan 06 2012
(PARI) a(n) = denominator(sigma(n)/numdiv(n)); \\ Michel Marcus, Apr 12 2016
(Magma) [Denominator(SumOfDivisors(n)/#Divisors(n)):n in [1..100]]; // Marius A. Burtea, Sep 08 2019

Crossrefs

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

Sequence in context: A353278 A328917 A265917 * A152443 A373368 A119804

Adjacent sequences: A057018 A057019 A057020 * A057022 A057023 A057024

Keyword

frac,nonn

Author

Henry Bottomley, Jul 21 2000

Status

approved