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A394055

Decimal expansion of the constant factor in the asymptotic for 2-dense numbers (A174973).

1, 2, 2, 4, 8, 3, 0

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OFFSET

1,2

COMMENTS

Decimal expansion of the constant c from the Weingartner's formula N(x) = c*x/log(x) + O(x/(log(x))^2), where N(x) is the number of 2-dense numbers not exceeding x.

This constant is mentioned in the Comments section of A174973.

LINKS

Table of n, a(n) for n=1..7.

Éric Saias, Etude du graphe divisoriel 5, Journal de Théorie des Nombres de Bordeaux, Vol. 36, No. 1 (2024), pp. 175-214. See p. 188, eq. (7.4).

Andreas Weingartner, On the constant factor in several related asymptotic estimates, Math. Comp., Vol. 88, No. 318 (2019), pp. 1883-1902; arXiv preprint, arXiv:1705.06349 [math.NT], 2017-2018.

Andreas Weingartner, The Schinzel-Szekeres function, Research in Number Theory, Vol. 11 (2025), Article 63; arXiv preprint, arXiv:2310.13038 [math.NT], 2023-2025.

FORMULA

Equals 1/(1 - exp(-gamma)) * Sum_{k 2-dense} (1/k) * (Sum_{p prime, p<=2*k} log(p)/(p-1) - log(k)) * Product_{p prime, p<=2*k} (1-1/p), where gamma is Euler's constant (A001620) (Weingartner, 2019, p. 1884, eq. (6)). - Amiram Eldar, Mar 22 2026

EXAMPLE

1.224830...

CROSSREFS

Cf. A001620, A174973, A327824, A392987.

Sequence in context: A065844 A131199 A112059 * A093094 A045777 A136534

Adjacent sequences: A394052 A394053 A394054 * A394056 A394057 A394058

KEYWORD

nonn,cons,more,new

AUTHOR

Omar E. Pol, Mar 14 2026

STATUS

approved

URL: https://oeis.org/A394055

⇱ A394055 - OEIS