a new sequence

[franktaw at netscape.net]

This suggests a couple of other sequences to me:
 
Smallest m such that n can be represented as the sum of distinct divisors of m in more than one way (offset 3):
 
6,12,12,6,12,12,6,12,12,12,12,12,24,24,24,18,18,18,18,20
 
Same, except the divisor sets must be disjoint (also offset 3):
 
6,12,12,6,12,12,18,20,20,12,12,12,24,24,24,18,36,20,20,36
 
These are related to A070172.
 
Obviously, each of these can only take on values in Emeric's sequence.
 
Franklin T. Adams-Watters
 
 
-----Original Message-----
From: Emeric Deutsch deutsch at duke.poly.edu


...
 
Values of n such that the number of distinct sums of 
distinct divisors of n is less than 2^tau(n) - 1 (clearly, 
the latter is the largest number of possible distinct sums). 
 
...
 
6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 
63, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, 
105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 
140, 144, 150, 154, 156, 160, 162, 165, 168, 170, 174, 176, 
180, 
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