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 A374778 #6 Jul 19 2024 14:28:11
%S A374778 1,4,6,12,10,24,14,32,27,8,22,72,26,56,60,80,34,54,38,120,4,88,46,192,
%T A374778 75,104,54,56,58,48,62,64,132,136,28,162,74,152,52,320,82,16,86,264,
%U A374778 135,184,94,160,49,30,204,104,106,216,20,64,76,232,118,720,122,248
%N A374778 Denominator of the mean abundancy index of the divisors of n.
%H A374778 Amiram Eldar, <a href="/A374778/b374778.txt">Table of n, a(n) for n = 1..10000</a>
%e A374778 For n = 2, n has 2 divisors, 1 and 2. Their abundancy indices are sigma(1)/1 = 1 and sigma(2)/2 = 3/2, and their mean abundancy index is (1 + 3/2)/2 = 5/4. Therefore a(2) = denominator(5/4) = 4.
%t A374778 f[p_, e_] := ((e+1)*p^2 - (e+2)*p + p^(-e))/((e+1)*(p-1)^2); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]
%o A374778 (PARI) a(n) = {my(f = factor(n), p, e); denominator(prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((e+1)*p^2 - (e+2)*p + p^(-e))/((e+1)*(p-1)^2)));}
%Y A374778 Cf. A374777 (numerators).
%K A374778 nonn,easy,frac
%O A374778 1,2
%A A374778 _Amiram Eldar_, Jul 19 2024