[seqfan] Re: GF for A083710 Number of partitions [...

David Wilson dwilson at gambitcomm.com
Wed Jun 10 15:15:27 CEST 2009


Or possibly

Number of partitions P of n where min(P) = gcd(P).

Joerg Arndt wrote:
> About to submit corrections:
> Replaced "summands" by the more common "parts" in alternative definition.
> Gave argument for the g.f.
> 
> Now:
> 
> %C A083710 Comment from Joerg Arndt, Jun 08 2009: Since the summand (part) which divides 
>                all the other summands is necessarily the smallest, an equivalent 
>                definition is: "Number of partitions of n such that smallest part
>                divides every part."
> 
> and:
> 
> %F A083710 Comment from Joerg Arndt, Jun 08 2009: Sequence has g.f. 1 + Sum_{n>=1} 
>                x^n/eta(x^n).  The g.f. for partitions into parts that are a multiple
>                of n is x^n/eta(x^n), now sum over n. 
> 
> 
> 
> 
> 
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