A272983 Decimal expansion of the normalized asymptotic mean of omega(m) when m is one of the values <= n taken by Euler's phi totient function.
2, 1, 8, 6, 2, 6, 3, 4, 6, 4, 8, 8, 5, 7, 5, 4, 8, 0, 8, 0, 5, 0, 8, 6, 7, 5, 7, 9, 5, 9, 0, 1, 0, 1, 7, 4, 3, 8, 7, 5, 8, 7, 9, 9, 5, 3, 8, 0, 1, 2, 5, 2, 4, 7, 7, 5, 6, 4, 6, 6, 4, 4, 5, 6, 8, 2, 1, 0, 6, 6, 2, 3, 4, 6, 5, 2, 1, 2, 1, 0, 4, 9, 2, 1, 1, 1, 0, 2, 0, 4, 2, 2, 0, 0, 0, 1, 3, 3
Offset: 1
Examples
2.186263464885754808050867579590101743875879953801252477564664456821...
References
- Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.7. Euler Totient Constants, pp. 115-119.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 16.
- Kevin Ford, The distribution of Totients
Programs
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Mathematica
digits = 98; F[x_?NumericQ] := NSum[((k+1)*Log[k+1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 1/2, 3/5}, WorkingPrecision -> digits + 10]; RealDigits[1/(1 - rho), 10, digits] // First
Formula
1/(1 - rho), where rho is A246746.