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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
OFFSET
1,2
COMMENTS
See A357845 for more details.
LINKS
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: A229421 A376012 A212718 * A051549 A245775 A277782
KEYWORD
nonn,frac
AUTHOR
Amiram Eldar, Oct 16 2022
STATUS
approved