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 A327574 Decimal expansion of the constant that appears in the asymptotic formula for average order of the infinitary divisors sum function (A049417). 1
 7, 3, 0, 7, 1, 8, 2, 4, 2, 1, 2, 7, 3, 8, 4, 2, 2, 5, 8, 3, 8, 9, 7, 5, 4, 6, 8, 1, 7, 3, 5, 3, 0, 1, 6, 1, 9, 5, 7, 2, 5, 6, 4, 3, 3, 8, 6, 1, 7, 2, 7, 8, 6, 9, 7, 0, 7, 3, 3, 6, 7, 6, 2, 3, 0, 1, 0, 7, 9, 8, 8, 3, 3, 2, 8, 0, 0, 5, 3, 4, 6, 3, 7, 0, 2, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The asymptotic mean of the infinitary abundancy index lim_{n->oo} (1/n) * Sum_{k=1..n} A049417(k)/k = 1.461436... is twice this constant. - Amiram Eldar, Jun 13 2020 REFERENCES Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54. LINKS Graeme L. Cohen and Peter Hagis, Jr., Arithmetic functions associated with infinitary divisors of an integer, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373-383. FORMULA Equals Limit_{k->oo} A327566(k)/k^2. Equals (1/2) * Product_{P} (1 + 1/(P*(P+1))), where P are numbers of the form p^(2^k) where p is prime and k >= 0 (A050376). EXAMPLE 0.730718242127384225838975468173530161957256433861727... MATHEMATICA \$MaxExtraPrecision = 1000; m = 1000; em = 10; f[x_] := Sum[Log[1 + x^(2^e)/(1 + 1/x^(2^e))], {e, 0, em}]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[(1/2) * Exp[NSum[Indexed[c, k]*PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]] CROSSREFS Cf. A049417, A050376, A327566. Cf. A013661 (corresponding constant for all divisors), A275480 (exponential), A306633 (unitary), A307160 (bi-unitary). Sequence in context: A245082 A019648 A232716 * A253905 A154159 A334060 Adjacent sequences:  A327571 A327572 A327573 * A327575 A327576 A327577 KEYWORD nonn,cons AUTHOR Amiram Eldar, Sep 17 2019 STATUS approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)