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

1,2

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.

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.

Example

1.53793986067512617495790860731212213674986310842521076221457235794311...

Mathematica

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

Prog

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

Crossrefs

Cf. A217660.

Sequence in context: A109694 A259068 A219336 * A135765 A222598 A221470

Adjacent sequences: A280232 A280233 A280234 * A280236 A280237 A280238

Keyword

cons,nonn

Author

Charles R Greathouse IV, Feb 25 2017

Status

approved