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).

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

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