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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.
1
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
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.7. Euler Totient Constants, pp. 115-119.
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 16.
FORMULA
1/(1 - rho), where rho is A246746.
EXAMPLE
2.186263464885754808050867579590101743875879953801252477564664456821...
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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved