[seqfan] Re: possible sequence

[Charles Greathouse]

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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