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A379616
Denominators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
3
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
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
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Dec 27 2024
STATUS
approved