[seqfan] Re: possible sequence

Charles Greathouse charles.greathouse at case.edu
Fri Mar 7 03:31:44 CET 2014


A better one: 2^25 * 3^227 * 7^28 has 140 digits. Any improvements would
have to be > 10^250.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Thu, Mar 6, 2014 at 9:06 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> 2^86 (26 digits) is conjectured to be the last 0-free power of two,
> see A007377.
>
> 2^184 * 3^88 (98 digits) seems to be the last 0-free 3-smooth number.
>
> 0-free numbers cannot contain both 2s and 5s, and the best {3, 5}-smooth
> number I can find is 3^28 * 5^90 (77 digits), so it looks like the largest
> 0-free 5-smooth number is 2^184 * 3^88 again.
>
> I don't know what the largest 0-free 7-smooth number is, but it's at
> least 2^298 * 3^69 * 7^7 (129 digits).
>
> One problem is that this sequence grows very quickly. Another is that no
> terms are actually known...! But it is interesting to think about.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> On Thu, Mar 6, 2014 at 7:57 PM, David Wilson <davidwwilson at comcast.net>wrote:
>
>> Largest zeroless p-smooth number for the first few primes p.
>>
>>
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