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 A379516 #7 Dec 24 2024 07:27:44
%S A379516 1,3,12,60,60,5,40,360,360,120,120,120,840,140,840,14280,42840,42840,
%T A379516 42840,8568,34272,34272,34272,11424,148512,49504,7072,35360,106080,
%U A379516 318240,159120,1750320,109395,656370,5250960,26254800,498841200,498841200,3491888400,3491888400
%N A379516 Denominators of the partial alternating sums of the reciprocals of the sum of unitary divisors function (A034448).
%H A379516 Amiram Eldar, <a href="/A379516/b379516.txt">Table of n, a(n) for n = 1..1000</a>
%H A379516 Olivier Bordellès and Benoit Cloitre, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Bordelles/bord14.html">An Alternating Sum Involving the Reciprocal of Certain Multiplicative Functions</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.6.3. See p. 4, eq. (vi).
%H A379516 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 4.9, pp. 28-29.
%F A379516 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A034448(k)).
%t A379516 usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma[1] = 1; Denominator[Accumulate[Table[(-1)^(n+1)/usigma[n], {n, 1, 50}]]]
%o A379516 (PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
%o A379516 list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / usigma(k); print1(denominator(s), ", "))};
%Y A379516 Cf. A034448, A064609, A370898, A379514, A379515 (numerators).
%K A379516 nonn,easy,frac
%O A379516 1,2
%A A379516 _Amiram Eldar_, Dec 23 2024