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

Thu Oct 6 19:38:21 CEST 2016

```Dear SeqFans,

I am pleased to inform you that
my paper "S-exponential numbers"
(connected, in particular, with
sequences A001694 and A209061)
has been published in Acta Arith.,
175.4 (2016), 385-395.

Best regards,
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Vladimir Shevelev [shevelev at exchange.bgu.ac.il]
Sent: 04 September 2015 14:27
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Numbers with squarefree exponents in      their   prime   factorizations

A better upper estimate for density of
A209061 is 1- sum_{k>=4}(1-|mu(k)|)*
(1/zeta(k+1) - 1/zeta(k))<0.95637

Best regards,

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Vladimir Shevelev [shevelev at exchange.bgu.ac.il]
Sent: 03 September 2015 18:20
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Numbers with squarefree exponents in their        prime   factorizations

An upper estimate for density of A209061
is 1-1/zeta(5)+1/zeta(4)=0.95955...

Best regards,
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Charles Greathouse [charles.greathouse at case.edu]
Sent: 02 September 2015 22:19
To: Sequence Fanatics Discussion list
Subject: [seqfan] Numbers with squarefree exponents in their prime      factorizations

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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```