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

[jean-paul allouche]

Congratulations Vladimir
and Shana Tova
jean-paul

Le 06/10/16 à 19:38, Vladimir Shevelev a écrit :
> 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,
> Vladimir
> ________________________________________
> 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,
> Vladimir
>
> ________________________________________
> 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,
> Vladimir
> ________________________________________
> 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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