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A327575 Decimal expansion of the constant that appears in the asymptotic formula for average order of an infinitary analog of Euler's phi function (A091732). 1
3, 2, 8, 9, 3, 5, 8, 3, 8, 8, 4, 0, 3, 3, 5, 5, 1, 6, 3, 5, 5, 7, 4, 8, 4, 8, 7, 3, 6, 5, 2, 2, 0, 2, 2, 9, 5, 7, 7, 0, 6, 6, 5, 2, 3, 7, 9, 4, 6, 9, 4, 0, 4, 4, 8, 0, 8, 4, 0, 3, 7, 9, 8, 7, 5, 2, 8, 1, 2, 4, 0, 0, 7, 7, 3, 7, 9, 6, 8, 7, 4, 8, 8, 3, 9, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.

LINKS

Table of n, a(n) for n=0..86.

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} A327572(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

0.328935838840335516355748487365220229577066523794694...

MATHEMATICA

$MaxExtraPrecision = 1500; m = 1500; 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. A091732, A050376, A327572.

Cf. A104141 (corresponding constant for phi), A065463 (unitary), A306071 (bi-unitary).

Sequence in context: A130918 A230432 A195305 * A328645 A021308 A274181

Adjacent sequences:  A327572 A327573 A327574 * A327576 A327577 A327578

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Sep 17 2019

STATUS

approved

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Last modified September 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)