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 A357846 Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203). 2
 1, 3, 12, 84, 84, 7, 56, 840, 10920, 32760, 32760, 32760, 32760, 16380, 32760, 1015560, 338520, 338520, 338520, 338520, 1354080, 4062240, 4062240, 4062240, 131040, 131040, 131040, 131040, 131040, 43680, 21840, 65520, 32760, 98280, 196560, 196560, 3734640, 3734640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A357845 for more details. LINKS Table of n, a(n) for n=1..38. Olivier Bordellès and Benoit Cloitre, An alternating sum involving the reciprocal of certain multiplicative functions, Journal of Integer Sequences, Vol. 16 (2013), Article 13.6.3. László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. FORMULA a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/sigma(k)), where sigma(k) = A000203(k). MATHEMATICA Denominator[Accumulate[Array[(-1)^(# + 1)/DivisorSigma[1, #] &, 60]]] PROG (PARI) lista(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / sigma(k); print1(denominator(s), ", "))}; (Python) from fractions import Fraction from sympy import divisor_sigma 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 CROSSREFS Cf. A000203, A068762, A357845 (numerators). Similar sequence: A104529, A212718, A357821. Sequence in context: A171186 A229421 A212718 * A051549 A245775 A277782 Adjacent sequences: A357843 A357844 A357845 * A357847 A357848 A357849 KEYWORD nonn,frac AUTHOR Amiram Eldar, Oct 16 2022 STATUS approved

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Last modified December 11 11:45 EST 2023. Contains 367725 sequences. (Running on oeis4.)