[seqfan] Re: An optimization problem with prime power factorization of integer x_i

[Vladimir Shevelev]

Thanks Rob, I  meant  A064547(prod{i=1,...,k}x_i)>=k  and carelessly took the "logarithm" which, generally speaking,  gives an error. In case  x = (2,3,4,5,6), the right restriction is not satisfied (A064547(720)=3<5).

Regards,
Vladimir

----- Original Message -----
From: Rob Pratt <Rob.Pratt at sas.com>
Date: Sunday, April 1, 2012 18:25
Subject: [seqfan] Re: An optimization problem with prime power factorization of integer x_i
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> Seems to fail first for k = 5, since x = (2,3,4,5,6) satisfies 
> the constraints and has a smaller product than (2,3,4,5,7).
> 
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-
> bounces at list.seqfan.eu] On Behalf Of Vladimir Shevelev
> Sent: Sunday, April 01, 2012 8:36 AM
> To: seqfan at list.seqfan.eu
> Subject: [seqfan] An optimization problem with prime power 
> factorization of integer x_i
> 
> Dear SeqFans,
> 
> 
> Let x_1, x_2,..., x_k be integers with the restrictions: 
> 2<=x_1<x_2<...<x_k, sum{i=1,...,k}A064547(x_i)>=k.  Let the goal function be Prod{i=1,...,k}x_i-->min.
> It is easy to see that the unique solution is {(x_1)^*,..., 
> (x_k)^*}, where {x_i}^* are the first k terms of A050376. If any 
> expert could verify how to get formally the solution or its 
> approximation, using the methods of integer programming?
> 
> Regards,
> Vladimir
> 
> 
>  Shevelev Vladimir‎
> 
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 Shevelev Vladimir‎