A380005 Decimal expansion of (7/3)*log(log(12)) - exp(gamma)*log(log(12))^2, where gamma is the Euler-Mascheroni constant (A001620).

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

Offset

0,1

Comments

Theorem 2 in Robin (1984) states that, for n >= 3, sigma(n)/n <= exp(gamma)*log(log(n)) + c/log(log(n)), with equality for n = 12, where sigma is the sum-of-divisors function (A000203) and c is the constant given by the present sequence. Cf. also Weisstein, eqs. (29) - (33).

References

G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, Journal de Mathématiques Pures et Appliquées, 63 (1984), pp. 187-213 (in French). See A073004 for a scanned copy.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Divisor Function, see eq. (31).

Formula

Equals (7/3)*log(A016635) - A073004*log(A016635)^2.

Example

0.64821364942179976272009425643532901899304479911015...

Mathematica

First[RealDigits[7/3*# - Exp[EulerGamma]*#^2, 10, 100]] & [Log[Log[12]]]

Crossrefs

Cf. A000203, A001620, A016635, A058209, A073004.

Sequence in context: A195487 A073746 A010496 * A199436 A035415 A197833

Adjacent sequences: A380002 A380003 A380004 * A380006 A380007 A380009

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jan 14 2025

Status

approved