Lcm of all numbers so far

From Number
Revision as of 20:29, 30 April 2009 by Vipul (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Definition

Let be a natural number. The lcm of all numbers so far for to , i.e., as:

.

Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A003418

Initial values

The values for are .

Growth

The lcm of all numbers so far has approximately exponential growth in . Moreover, it is not strictly increasing as a function of , and it increases in value only at prime powers. At the prime power , it gets multiplied by .

It is the exponential of the second Chebyshev function. More details on the growth are to be found in the page on the second Chebyshev function.

Relation with other functions

Logarithm

The logarithm of the lcm of all numbers so far is equal to the second Chebyshev function.