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A379620
Denominators of the partial sums of the reciprocals of the alternating sum of divisors function (A206369).
3
1, 1, 2, 6, 12, 12, 4, 20, 140, 35, 70, 105, 140, 420, 840, 9240, 18480, 18480, 55440, 55440, 55440, 55440, 55440, 11088, 1584, 1584, 7920, 7920, 55440, 55440, 11088, 1584, 7920, 3960, 990, 6930, 13860, 13860, 27720, 27720, 1386, 2772, 2772, 13860, 3465, 6930, 79695
OFFSET
1,3
LINKS
László Tóth, A survey of the alternating sum-of-divisors function, Acta Universitatis Sapientiae, Mathematica, Vol. 5, No. 1 (2013), pp. 93-107. See p. 101, eq. (17).
László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.14, p. 35.
FORMULA
a(n) = denominator(Sum_{k=1..n} 1/A206369(k)).
MATHEMATICA
f[p_, e_] := Sum[(-1)^(e-k)*p^k, {k, 0, e}]; beta[1] = 1; beta[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/beta[n], {n, 1, 50}]]]
PROG
(PARI) beta(n) = {my(f = factor(n)); prod(i=1, #f~, p = f[i, 1]; e = f[i, 2]; sum(k = 0, e, (-1)^(e-k)*p^k)); }
list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / beta(k); print1(denominator(s), ", "))};
CROSSREFS
Cf. A206369, A370905, A370906, A379619 (numerators), A379622.
Sequence in context: A354421 A069491 A127698 * A379518 A130503 A278232
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Dec 27 2024
STATUS
approved