A280235 Constant appearing in the Nicolas-Robin bound for the divisor function.

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

Offset: 1

Author

Charles R Greathouse IV, Feb 25 2017

Keywords

• cons
• nonn

Comments

The number of divisors of n is at most 2^(k * log n/log log n) where k is this constant. Equality is attained precisely at n = 6983776800.

Examples

			1.53793986067512617495790860731212213674986310842521076221457235794311...
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..150
• J. L. Nicolas and G. Robin, Majorations explicites pour le nombre de diviseurs de N, Canadian Mathematical Bulletin 26 (1983), pp. 485-492.

Crossrefs

Cf. A217660.

Programs

Mathematica

L = Log[6983776800]; RealDigits[2 * Log[48] * Log[L] / L / Log[2], 10, 89][[1]] (* Indranil Ghosh, Mar 12 2017 *)

PARI

L=log(6983776800); 2*log(48)*log(L)/L/log(2)