A280235 - OEIS

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

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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 *)