sum of unit fractions

[Paul D. Hanna]

Sorry, had a transcription error in my last email. 
All sets of unit fractions adding to unity given were correct 
except the simplest sets for cases n=2, 3: 
> {2,3,4,6}
> {5,8,9,10,15,18,20,24}
which of course should have been: 
{2,3,6}
{4,5,8,9,10,15,18,20,24}
 
This correction makes the sequences mentioned begin:
Initial least terms: 
{1,2,5,7,17,29,...}
Number of terms: 
{1,3,9,24,73,182,...}
Sum of terms: 
 {1,11,113,835,7524,48639,...}
 
Also, I wonder if this observation continues to hold for all cases:
> Assuming that the sets of unit fractions that sum to n are 
> accumulative, so that the (n+1)-th set contains the n-th set, 
> then we can separate these into subsets of unit fractions that sum 
> to unity. 
 
Paul