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

Author

Paolo Xausa, Jan 14 2025

Keywords

• nonn
• cons
• easy

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).

Examples

			0.64821364942179976272009425643532901899304479911015...
		

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).

Crossrefs

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

Programs

Mathematica

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

Formula

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