[seqfan] Re: A045655

David Wilson davidwwilson at comcast.net
Mon Jan 2 00:24:39 CET 2012


Or I could get my index variable correct (Alzheimer's is hell):

A045655(n) = sum(d|n, d*A027375(d)) = sum(d|n, d^2*A001037(d))

where

sum(d|n, A027375(d)) = 2^n.

sum(d|n, A001037(d)) = A000031(n).


On 1/1/2012 5:40 PM, David Wilson wrote:
> On 1/1/2012 3:52 PM, Olivier Gerard wrote:
>> Hello,
>>
>> The comment by Geoffrey is indeed correct but his various programs were
>> inefficient or relying on obsolete librairies not loaded (i.e.
>> Combinatorica).
>>
>> I have replaced it by another version and added a few comments.
>>
>> There should be a formula in the form of a sum of squares giving the
>> general term of the sequence instead of brute force enumeration.
>>
>> Olivier
>>
> Olivier:
>
> I think you are looking for
>
> A045655(n) = sum(d|n, n*A027375(n)) = sum(d|n, n^2*A001037(n))
>
> where
>
> sum(d|n, A027375(n)) = 2^n.
>
> sum(d|n, A001037(n)) = A000031(n).
>
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