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 A379620 #9 Jan 08 2025 11:41:53
%S A379620 1,1,2,6,12,12,4,20,140,35,70,105,140,420,840,9240,18480,18480,55440,
%T A379620 55440,55440,55440,55440,11088,1584,1584,7920,7920,55440,55440,11088,
%U A379620 1584,7920,3960,990,6930,13860,13860,27720,27720,1386,2772,2772,13860,3465,6930,79695
%N A379620 Denominators of the partial sums of the reciprocals of the alternating sum of divisors function (A206369).
%H A379620 Amiram Eldar, <a href="/A379620/b379620.txt">Table of n, a(n) for n = 1..1000</a>
%H A379620 László Tóth, <a href="https://doi.org/10.2478/ausm-2014-0007">A survey of the alternating sum-of-divisors function</a>, Acta Universitatis Sapientiae, Mathematica, Vol. 5, No. 1 (2013), pp. 93-107. See p. 101, eq. (17).
%H A379620 László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.14, p. 35.
%F A379620 a(n) = denominator(Sum_{k=1..n} 1/A206369(k)).
%t A379620 f[p_, e_] := Sum[(-1)^(e-k)*p^k, {k, 0, e}]; beta[1] = 1; beta[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/beta[n], {n, 1, 50}]]]
%o A379620 (PARI) beta(n) = {my(f = factor(n)); prod(i=1, #f~, p = f[i, 1]; e = f[i, 2]; sum(k = 0, e, (-1)^(e-k)*p^k)); }
%o A379620 list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / beta(k); print1(denominator(s), ", "))};
%Y A379620 Cf. A206369, A370905, A370906, A379619 (numerators), A379622.
%K A379620 nonn,easy,frac
%O A379620 1,3
%A A379620 _Amiram Eldar_, Dec 27 2024