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 A357846 #10 Oct 17 2022 01:43:30 %S A357846 1,3,12,84,84,7,56,840,10920,32760,32760,32760,32760,16380,32760, %T A357846 1015560,338520,338520,338520,338520,1354080,4062240,4062240,4062240, %U A357846 131040,131040,131040,131040,131040,43680,21840,65520,32760,98280,196560,196560,3734640,3734640 %N A357846 Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203). %C A357846 See A357845 for more details. %H A357846 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. %H A357846 László Tóth, <a href="https://www.emis.de/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. %F A357846 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/sigma(k)), where sigma(k) = A000203(k). %t A357846 Denominator[Accumulate[Array[(-1)^(# + 1)/DivisorSigma[1, #] &, 60]]] %o A357846 (PARI) lista(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / sigma(k); print1(denominator(s), ", "))}; %o A357846 (Python) %o A357846 from fractions import Fraction %o A357846 from sympy import divisor_sigma %o A357846 def A357846(n): return sum(Fraction(1 if k&1 else -1, divisor_sigma(k)) for k in range(1,n+1)).denominator # _Chai Wah Wu_, Oct 16 2022 %Y A357846 Cf. A000203, A068762, A357845 (numerators). %Y A357846 Similar sequence: A104529, A212718, A357821. %K A357846 nonn,frac %O A357846 1,2 %A A357846 _Amiram Eldar_, Oct 16 2022