A379618 Denominators of the partial alternating sums of the reciprocals of the sum of bi-unitary divisors function (A188999).

1, 3, 12, 60, 60, 5, 40, 120, 24, 72, 72, 360, 2520, 1260, 2520, 7560, 7560, 1512, 7560, 7560, 30240, 30240, 30240, 6048, 78624, 78624, 393120, 78624, 393120, 393120, 196560, 196560, 98280, 10920, 21840, 109200, 2074800, 691600, 691600, 6224400, 6224400, 12448800

Offset

1,2

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 4.13, p. 34.

Formula

a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A188999(k)).

Mathematica

f[p_, e_] := (p^(e+1) - 1)/(p - 1) - If[OddQ[e], 0, p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[(-1)^(n+1)/bsigma[n], {n, 1, 50}]]]

Prog

(PARI) bsigma(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1] - 1) - if(!(f[i, 2] % 2), f[i, 1]^(f[i, 2]/2))); }
list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / bsigma(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A188999, A307159, A370904, A379616, A379617 (numerators).

Sequence in context: A201013 A379616 A379514 * A379516 A065080 A114419

Adjacent sequences: A379615 A379616 A379617 * A379619 A379620 A379621

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 27 2024

Status

approved