# [seqfan] Re: Typo in B-file for A063539

jean-paul allouche jean-paul.allouche at imj-prg.fr
Fri Apr 10 22:17:00 CEST 2020

```Dear all

I am not sure that my message below came through.

Actually there is something more: the density being
(1 - ln 2), this implies that the n-th term of the sequence
is equivalent to Cn with C = 1/(1-ln (2)) which is about 3.259
(so that it is not 3.7642*n as indicated in the Formula Section.
Since I have a bad internet connection, it would be good if
someone could have a quick check and make the corresponding
changes in A063539.

best wishes
jean-paul

Le 03/04/2020 à 18:29, jean-paul allouche a écrit :
> Hi
>
> He told me that this is, e.g., Exercise 28 (with proof) in his book
> with Jie Wu:
>
> # GÉRALD TENENBAUM
> <https://www.belin-education.com/gerald-tenenbaum>, JIE WU
> <https://www.belin-education.com/jie-wu>
> #
>
> #
>
>
>  Théorie analytique et probabiliste des nombres
>
>
>    307 exercices corrigés
>
>
> I double-checked: this is indeed Exercise 28 on Page 26, the solution
> can be found on Page 34. Everything is in French but this should not be
> a problem. Note that the first few pages of the book (including the two
> pages above) are freely accessible on the site of the publisher:
> https://www.belin-education.com/theorie-analytique-et-probabiliste-des-nombres
>
> by clicking on the cover page.
>
> best wishes
> jean-paul
>
>
>
>
> Le 02/04/2020 à 18:34, Allan Wechsler a écrit :
>> A063539 collects numbers whose largest prime factor is less than the
>> square
>> root. For example, 29925 = 3^2 * 5^2 * 7 * 19, and 19^2 is only 361,
>> much
>> smaller than 29925.
>>
>> An interesting feature of this sequence is that it has constant
>> asymptotic
>> density; HAKMEM item 29 (Schroeppel) identifies the density as (1 -
>> ln 2),
>> without proof.
>>
>> Because of this intriguing feature, it's interesting to look at the
>> graph
>> (which of course looks like a straight line), and this reveals an odd
>> blot
>> under the line, which I have traced to a typo in the B-file.
>>
>> A(7910) ought to be 29925 (the example I gave above), but is instead
>> given
>> as 9925, which should not be in the sequence because its largest prime
>> factor is 397.
>>
>> I wonder how typos like this can creep in -- the text of the B-file
>> ought
>> to be copied directly from program output, and never pass through human
>> editorial hands which might drop a digit, as seems to have happened
>> here.
>>
>> (Also, the comments should include the slope of the line, ideally with a
>> citation to someplace that proves the identity.)
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/

```