[SPAM?]: RE: A129755 (??!!)

[Peter Pein]

Andrew Plewe schrieb:
> Well, I'll stand up for lowly k-gonal numbers as being of interest (to me,
> anyways). Generally, there are two questions I'd like to answer. Someone may
> have already answered them, if so I haven't found those answers yet:
> 
> 
> 1.) If you know the factors of some composite integer k, can you find all
> the representations of k as a sum of constant-spaced integers? For instance,
> 35 = 5*7, has at least the following representations:
> {7 7 7 7 7; 5 6 7 8 9; 3 5 7 9 11; 1 4 7 10 13; 5 5 5 5 5 5 5; 2 3 4 5 6 7
> 8}. Is that all of them? Is there an algorithmic way to determine all of
> them? I believe the answer to that last question is yes, but I haven't
> formulated a complete method yet. I have a vague inkling that the "ease" of
> factoring k may have something to do with the ratio of the number of these
> represenations of k to k, but it's just an idea at this point.
...
> 	-Andrew Plewe-
> 

Hi Andrew,

if we allow only positive summands (no "0+35" for instance), this leads to
A049990.

Peter