[seqfan] Re: Numbers that are divisible by the product of their digits

[Antti Karttunen]

On Sat, Jun 10, 2017 at 6:53 AM, <seqfan-request at list.seqfan.eu> wrote:

>
>
> Message: 4
> Date: Tue, 6 Jun 2017 02:47:24 -0400
> From: Charles Greathouse <charles.greathouse at case.edu>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Numbers that are divisible by the product of their
>         digits
> Message-ID:
>         <CAAkfSG+Oc4MPRvLscOodsxLZ3AipF6tX=jZsy
> t4L9bkWMcvAEg at mail.gmail.com>
> Content-Type: text/plain; charset="UTF-8"
>
> A007602 is the sequence of numbers that are divisible by the product of
> their digits. Does anyone know how this sequence grows?
>
> The sequence is infinite, as it contains the repunits. You can get a very
> weak bound by taking numbers with two 3s and 9k+3 1s: this shows there are
> at least n^3/54 +O(n^2) terms with up to n digits, so log a(n) << n^(1/3).
> But surely more is true?
>
>
And concerning also Hugo van Sanden's post, (extending it to other bases):
http://list.seqfan.eu/pipermail/seqfan/2017-June/017692.html
here is the factorial base analog of the sequence:

https://oeis.org/A286590

This sequence is also infinite for sure because now it is A007489 that
serves the role of repunits. I don't know whether it is any more or less
interesting to analyze than the fixed-base variants.


Best regards,

Antti



> My interest comes from a recent submission I just approved, A288069, which
> are the quotients in this sequence. The quotients go to infinity, but I
> can't give a rate of growth on the quotients without knowing the rate of
> growth of the underlying sequence.
>
> Charles Greathouse
> Case Western Reserve University
>
>
>