This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A057021 #42 Jul 18 2025 14:46:23
%S A057021 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 A057021 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 A057021 1,1
%N A057021 Denominator of (sum of divisors of n / number of divisors of n).
%C A057021 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 A057021 a(A069081(n)) = 2. - _Bernard Schott_, Sep 19 2019
%H A057021 Reinhard Zumkeller, <a href="/A057021/b057021.txt">Table of n, a(n) for n = 1..10000</a>
%F A057021 a(n) = A057020(n)*A000005(n)/A000203(n) = A000005(n)/A009205(n).
%e A057021 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 A057021 with(numtheory): seq(denom(sigma(n)/tau(n)), n=1..70) ; # _Zerinvary Lajos_, Jun 04 2008
%t A057021 Denominator[Table[(Plus @@ Divisors[n])/Length[Divisors[n]], {n, 70}]] (* _Alonso del Arte_, Feb 24 2006 *)
%o A057021 (Haskell)
%o A057021 import Data.Ratio ((%), denominator)
%o A057021 a057021 n = denominator $ a000203 n % a000005 n
%o A057021 -- _Reinhard Zumkeller_, Jan 06 2012
%o A057021 (PARI) a(n) = denominator(sigma(n)/numdiv(n)); \\ _Michel Marcus_, Apr 12 2016
%o A057021 (Magma) [Denominator(SumOfDivisors(n)/#Divisors(n)):n in [1..100]]; // _Marius A. Burtea_, Sep 08 2019
%o A057021 (SageMath) [denominator(sigma(n, 1)/sigma(n, 0)) for n in range(1, 71)] # _Stefano Spezia_, Jul 18 2025
%Y A057021 Cf. A000005, A000203, A009205, A054025, A057020 (numerator), A057022, A069081.
%K A057021 frac,nonn
%O A057021 1,2
%A A057021 _Henry Bottomley_, Jul 21 2000