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%I #16 Jun 10 2020 04:48:46
%S 7,5,2,8,3,8,7,4,1,0,0,2,2,9,4,3,1,1,5,4,3,3,3,0,9,5,1,5,5,3,0,4,1,2,
%T 7,6,5,1,9,5,2,5,4,6,7,5,6,5,2,2,1,0,8,5,8,7,7,9,0,3,2,8,7,8,6,8,1,2,
%U 5,2,2,6,0,5,5,8,1,4,8,7,8,4,7,7,4,1,8,6,0,4,7,8,2,5,8,0,7,0,0,1,1,9,9,4,1,3
%N Decimal expansion of the constant c in the asymptotic formula for the partial sums of the bi-unitary divisors sum function, A307159(k) ~ c*k^2.
%C The asymptotic mean of the bi-unitary abundancy index lim_{n->oo} (1/n) * Sum_{k=1..n} A188999(k)/k = 2*c = 1.505677... - _Amiram Eldar_, Jun 10 2020
%D D. Suryanarayana and M. V. Subbarao, Arithmetical functions associated with the biunitary k-ary divisors of an integer, Indian J. Math., Vol. 22 (1980), pp. 281-298.
%H László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating sums concerning multiplicative arithmetic functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1, section 4.13.
%F Equals (zeta(2)*zeta(3)/2)* Product_{p}(1 - 2/p^3 + 1/p^4 + 1/p^5 - 1/p^6).
%e 0.75283874100229431154333095155304127651952546756522...
%t $MaxExtraPrecision = 1000; nm=1000; c = Rest[CoefficientList[Series[Log[1 - 2*x^3 + x^4 + x^5 - x^6],{x,0,nm}],x] * Range[0, nm]]; RealDigits[(Zeta[2]*Zeta[3]/2) * Exp[NSum[Indexed[c, k] * PrimeZetaP[k]/k, {k, 2, nm}, NSumTerms -> nm, WorkingPrecision -> nm]], 10, 100][[1]]
%Y Cf. A188999, A306071, A306072, A307159.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Mar 27 2019
%E More terms from _Vaclav Kotesovec_, May 29 2020
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