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

[Rob Pratt]

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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