A379622 Denominators of the partial alternating sums of the reciprocals of the alternating sum of divisors function (A206369).

1, 1, 2, 6, 12, 12, 12, 60, 420, 210, 105, 210, 140, 420, 840, 9240, 18480, 2640, 7920, 7920, 7920, 7920, 7920, 7920, 55440, 55440, 11088, 3696, 528, 528, 2640, 18480, 3696, 924, 616, 1848, 5544, 5544, 2772, 6930, 27720, 27720, 27720, 27720, 27720, 27720, 637560

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

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)^(k+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)^(n+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)^(k+1) / beta(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A206369, A370905, A370906, A379620, A379621 (numerators).

Sequence in context: A074385 A057340 A092427 * A379520 A392059 A058198

Adjacent sequences: A379619 A379620 A379621 * A379623 A379624 A379625

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 27 2024

Status

approved