cp's OEIS Frontend

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.

A357846 Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203).

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%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