A379616 Denominators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).

1, 3, 12, 60, 20, 30, 120, 40, 40, 360, 360, 72, 504, 126, 504, 1512, 1512, 7560, 1512, 7560, 30240, 30240, 30240, 30240, 393120, 393120, 393120, 393120, 393120, 393120, 196560, 28080, 14040, 4680, 9360, 46800, 889200, 889200, 6224400, 6224400, 889200, 1778400

Offset

1,2

Links

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

V. Sitaramaiah and M. V. Subbarao, Asymptotic formulae for sums of reciprocals of some multiplicative functions, J. Indian Math. Soc., Vol. 57 (1991), pp. 153-167.

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/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/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 / bsigma(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A188999, A307159, A370904, A379615 (numerators), A379618.

Sequence in context: A020102 A277179 A201013 * A379514 A379618 A379516

Adjacent sequences: A379613 A379614 A379615 * A379617 A379618 A379619

Keyword

nonn,easy,frac,new

Author

Amiram Eldar, Dec 27 2024

Status

approved