A308042 - OEIS

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A308042

Decimal expansion of the asymptotic mean of d_3(k)/ud_3(k), where d_3(k) is the number of ordered factorizations of k as product of 3 divisors (A007425) and ud_3(k) = 3^omega(k) is the unitary analog of d_3 (A074816).

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

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

OFFSET

1,1

LINKS

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

Meselem Karras and Abdallah Derbal, Mean value of an arithmetic function associated with the Piltz divisor function, Asian-European Journal of Mathematics, Vol. 13, No. 3 (2018), 2050062.

FORMULA

Equals Product_{p prime} ((1 - 1/p) * (2 + (1 - 1/p)^(-3))/3).

EXAMPLE

2.22416248380186958442174889454690037857600080851428...

MATHEMATICA

$MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{6, -16, 64/3, -32/3}, {0, 8, 32, 224/3}, m]; RealDigits[Exp[NSum[Indexed[c, n]*PrimeZetaP[n]/n/2^n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

PROG

(PARI) prodeulerrat((1 - 1/p) * (2 + (1 - 1/p)^(-3))/3) \\ Amiram Eldar, Sep 16 2024

CROSSREFS

Cf. A001221, A007425, A074816, A307869.

Sequence in context: A071470 A197116 A104461 * A335694 A084862 A327987

Adjacent sequences: A308039 A308040 A308041 * A308043 A308044 A308045

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, May 10 2019

STATUS

approved