OFFSET
1,2
COMMENTS
Also the asymptotic mean of ratio between the number of divisors and the number of unitary divisors of the integers.
LINKS
Ouarda Bouakkaz and Abdallah Derbal, The mean value of the function d(n)/d*(n) in arithmetic progressions, Notes on Number Theory and Discrete Mathematics, Vol. 29, No. 3 (2023), pp. 445-453.
Mihoub Bouderbala, On a sum of a multiplicative function linked to the divisor function over the set of integers B-multiple of 5, Communications in Mathematics, Vol. 31, No. 1 (2023), pp. 369-374; arXiv preprint, arXiv:2212.05549 [math.NT], 2022.
Abdallah Derbal and Meselem Karras, Valeurs moyennes d'une fonction liée aux diviseurs d'un nombre entier, C. R. Acad. Sci. Paris, Ser. I, Vol. 354, No. 6 (2016), pp. 555-558.
Mark Kac, Statistical Independence in Probability, Analysis and Number Theory, Carus Monograph 12, Math. Assoc. Amer., 1959, p. 79.
FORMULA
Equals Product_{p prime} 1 + 1/(2 * p * (p-1)).
Equals (Pi^2/6) * Product_{p prime} 1 - 1/(2 * p^2) + 1/(2 * p^3).
EXAMPLE
1.42765653542483988311752393968732790409373362807443...
MATHEMATICA
$MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{4, -6, 4}, {0, 4, 12}, 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/(2 * p * (p-1))) \\ Amiram Eldar, Mar 17 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, May 02 2019
EXTENSIONS
More terms from Vaclav Kotesovec, May 29 2020
STATUS
approved