login
A057021
Denominator of (sum of divisors of n / number of divisors of n).
21
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
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
KEYWORD
frac,nonn
AUTHOR
Henry Bottomley, Jul 21 2000
STATUS
approved