cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

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

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Author

Amiram Eldar, Sep 17 2019

Keywords

Examples

			0.328935838840335516355748487365220229577066523794694...
		

References

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

Crossrefs

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

Programs

  • 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]]

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).
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