[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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