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%I #10 Oct 17 2022 01:43:30
%S 1,3,12,84,84,7,56,840,10920,32760,32760,32760,32760,16380,32760,
%T 1015560,338520,338520,338520,338520,1354080,4062240,4062240,4062240,
%U 131040,131040,131040,131040,131040,43680,21840,65520,32760,98280,196560,196560,3734640,3734640
%N Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203).
%C See A357845 for more details.
%H 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 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 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/sigma(k)), where sigma(k) = A000203(k).
%t Denominator[Accumulate[Array[(-1)^(# + 1)/DivisorSigma[1, #] &, 60]]]
%o (PARI) lista(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / sigma(k); print1(denominator(s), ", "))};
%o (Python)
%o from fractions import Fraction
%o from sympy import divisor_sigma
%o 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 Cf. A000203, A068762, A357845 (numerators).
%Y Similar sequence: A104529, A212718, A357821.
%K nonn,frac
%O 1,2
%A _Amiram Eldar_, Oct 16 2022