# [seqfan] Re: Numbers with squarefree exponents in their prime factorizations

David Corneth davidacorneth at gmail.com
Thu Sep 3 11:39:05 CEST 2015

```An upperbound is found by using density of numbers of the form 2^4 * (2k +
1), which is 1/32, so an upperbound is 1 - 1/32 = 0.96875. This can be
wittled down by excluding numbers of the form 81 * (3m + 1) or 81 * (3m +
2). But numbers that are both of the form 2^4 * (2k + 1) and [81 * (3m + 1)
or 81 * (3m + 2)].
The intersections are values of k an m such that 32k - 243m = 65 or 32k -
243m = 146. Does that for an upperbound?

On Wed, Sep 2, 2015 at 9:19 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I was looking at sequence A209061 today and wondered what its density was.
> With A046100 as a subsequence it's at least 1/zeta(4) = 0.92..., of course.
> But I can't quite figure out what Euler product to use here -- can anyone
> help out to improve the sequence?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
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```