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 A379366 #6 Dec 22 2024 16:53:48
%S A379366 1,3,15,120,360,360,4680,936,6552,19656,19656,12285,61425,61425,61425,
%T A379366 982800,10810800,10810800,399999600,399999600,30769200,30769200,
%U A379366 30769200,30769200,399999600,79999920,239999760,239999760,4559995440,911999088,55631944368,27815972184
%N A379366 Denominators of the partial alternating sums of the reciprocals of Pillai's arithmetical function (A018804).
%H A379366 Amiram Eldar, <a href="/A379366/b379366.txt">Table of n, a(n) for n = 1..1000</a>
%H A379366 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 4.5, pp. 23-24.
%F A379366 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A018804(k)).
%t A379366 f[p_, e_] := (e*(p-1)/p + 1)*p^e; pillai[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[(-1)^(n+1)/pillai[n], {n, 1, 50}]]]
%o A379366 (PARI) pillai(n) = {my(f=factor(n)); prod(i=1, #f~, (f[i,2]*(f[i,1]-1)/f[i,1] + 1)*f[i,1]^f[i,2]);}
%o A379366 list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / pillai(k); print1(denominator(s), ", "))};
%Y A379366 Cf. A018804, A272718, A370895, A379364, A379365 (numerators).
%K A379366 nonn,easy,frac
%O A379366 1,2
%A A379366 _Amiram Eldar_, Dec 21 2024