A057021 - OEIS

%I #39 Sep 08 2022 08:45:01

%S 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,

%T 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,

%U 1,1

%N Denominator of (sum of divisors of n / number of divisors of n).

%C a(n) = 1 when n is listed in A003601, a(n) > 1 when n is listed in A049642. - _Alonso del Arte_, Jan 31 2006

%C a(A069081(n)) = 2. - _Bernard Schott_, Sep 19 2019

%H Reinhard Zumkeller, <a href="/A057021/b057021.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%p with(numtheory): seq(denom(sigma(n)/tau(n)), n=1..70) ; # _Zerinvary Lajos_, Jun 04 2008

%t Denominator[Table[(Plus @@ Divisors[n])/Length[Divisors[n]], {n, 70}]] (* _Alonso del Arte_, Feb 24 2006 *)

%o (Haskell)

%o import Data.Ratio ((%), denominator)

%o a057021 n = denominator $ a000203 n % a000005 n

%o -- _Reinhard Zumkeller_, Jan 06 2012

%o (PARI) a(n) = denominator(sigma(n)/numdiv(n)); \\ _Michel Marcus_, Apr 12 2016

%o (Magma) [Denominator(SumOfDivisors(n)/#Divisors(n)):n in [1..100]]; // _Marius A. Burtea_, Sep 08 2019

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

%K frac,nonn

%O 1,2

%A _Henry Bottomley_, Jul 21 2000