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 A379520 #7 Dec 24 2024 07:29:03
%S A379520 1,1,2,6,12,12,12,84,168,168,840,840,280,840,105,105,1680,1680,5040,
%T A379520 5040,5040,5040,55440,55440,55440,55440,720720,80080,80080,80080,
%U A379520 240240,7447440,7447440,3723720,620620,3723720,11171160,11171160,1396395,5585580,2234232,2234232
%N A379520 Denominators of the partial alternating sums of the reciprocals of the unitary totient function (A047994).
%H A379520 Amiram Eldar, <a href="/A379520/b379520.txt">Table of n, a(n) for n = 1..1000</a>
%H A379520 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 4.10, pp. 30-31.
%F A379520 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A047994(k)).
%t A379520 uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); uphi[1] = 1; Denominator[Accumulate[Table[(-1)^(n+1)/uphi[n], {n, 1, 50}]]]
%o A379520 (PARI) uphi(n) = {my(f = factor(n)); prod(i = 1, #f~, -1 + f[i, 1]^f[i, 2]);}
%o A379520 list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / uphi(k); print1(denominator(s), ", "))};
%Y A379520 Cf. A047994, A177754, A370899, A379518, A379519 (numerators).
%K A379520 nonn,easy,frac
%O A379520 1,3
%A A379520 _Amiram Eldar_, Dec 24 2024