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A234614 Decimal expansion of constant related to the growth of the number of totients. 1
8, 1, 7, 8, 1, 4, 6, 4, 0, 0, 8, 3, 6, 3, 2, 2, 3, 1, 5, 2, 5, 5, 9, 6, 8, 0, 0, 9, 0, 2, 9, 6, 5, 6, 0, 3, 8, 6, 4, 8, 5, 2, 9, 8, 2, 3, 7, 8, 9, 9, 1, 7, 8, 6, 3, 8, 6, 1, 2, 6, 3, 2, 0, 4, 2, 9, 7, 9, 1, 0, 0, 5, 2, 4, 5, 4, 9, 6, 4, 2, 1, 9, 6, 7, 0, 4, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let f_k(x) = x * exp(k (log log log x)^2)/log x. Maier & Pomerance show that, for any e > 0, f_{c-e}(x) << g(x) << f_{c+e}(x) where g(x) gives the number of totients less than x and c is this constant. Loosely, this means f_c(A007617(n)) is about n.

LINKS

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

Helmut Maier and Carl Pomerance, On the number of distinct values of Euler's phi-function, Acta Arithmetica 49 (1988), pp. 263-275.

FORMULA

See Maier & Pomerance p. 264.

Equals -1/(2*log(c0)), where c0 is a constant whose decimal expansion is A246746. - Amiram Eldar, Jun 19 2018

EXAMPLE

0.81781464008363223152559680090296560386485298237899...

MATHEMATICA

digits = 101; 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, 5/10, 6/10}, WorkingPrecision -> digits + 10]; RealDigits[rho, 10, digits] // First ; RealDigits[-1/2/Log[rho], 10, 90][[1]] (* after Jean-Fran├žois Alcover at A246746 *)

CROSSREFS

Cf. A007617, A246746.

Sequence in context: A200277 A242024 A159642 * A246750 A199872 A143548

Adjacent sequences:  A234611 A234612 A234613 * A234615 A234616 A234617

KEYWORD

nonn,cons

AUTHOR

Charles R Greathouse IV, Dec 28 2013

EXTENSIONS

a(8) corrected and more terms added by Amiram Eldar, Jun 19 2018

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)