(Almost)Consecutive-Integer Egyptian-Fraction Sum =1

[Leroy Quet]

>[posted also to sci.math.]
>
>I was led to this question by considering (m+1)-sided polygons where all 
>but one of the sides are that of a k-gon, a (k+1)-gon, a (k+2)-gon,..., 
>an (k+m)-gon.


Whooops. Should be "(m+2)-sided polygons".

Leroy

>
>But I wanted the final angle to be that of an n-gon, for some positive 
>integer n.
>
>For example,
>
>1/3 + 1/4 + 1/5 + 1/6 + 1/20 = 1.
>
>So, my question is,
>
>which integers n are such that:
>
>1/k + 1/(k+1) + 1/(k+2) +....+1/(k+m) + 1/n = 1 ?
>
>What is the sequence of such n's? Is it in the EIS?
>
>thanks,
>Leroy Quet