A327838 - OEIS

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A327838

Decimal expansion of the asymptotic mean of the exponential totient function (A072911).

1, 2, 5, 2, 7, 0, 7, 7, 8, 5, 3, 7, 5, 4, 4, 6, 1, 2, 6, 0, 5, 3, 7, 5, 0, 7, 5, 1, 9, 3, 4, 2, 8, 3, 0, 6, 0, 4, 3, 9, 2, 3, 7, 9, 6, 7, 1, 0, 8, 9, 1, 5, 3, 7, 3, 7, 4, 4, 8, 4, 9, 5, 1, 4, 0, 2, 9, 5, 7, 8, 3, 4, 3, 8, 6, 5, 4, 4, 2, 8, 6, 5, 0, 9, 5, 3, 7

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..87.

László Tóth, On certain arithmetic functions involving exponential divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 24 (2004), pp. 285-294.

FORMULA

Equals lim_{m->oo} (1/m) Sum_{k=1..m} A072911(k).

Equals Product_{p prime} (1 + Sum_{e >= 3} (phi(e) - phi(e-1))/p^e), where phi is the Euler totient function (A000010).

EXAMPLE

1.252707785375446126053750751934283060439237967108915...

MATHEMATICA

$MaxExtraPrecision = 500; m = 500; f[x_] := Log[1 + Sum[x^e * (EulerPhi[e] - EulerPhi[e - 1]), {e, 3, m}]]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[Exp[f[1/2] + NSum[Indexed[c, k]*(PrimeZetaP[k] - 1/2^k)/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

CROSSREFS

Cf. A000010, A072911, A322887, A327837, A361013.

Sequence in context: A067948 A142148 A142583 * A086956 A198570 A190290

Adjacent sequences: A327835 A327836 A327837 * A327839 A327840 A327841

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Sep 27 2019

STATUS

approved