a new sequence

[Emeric Deutsch]

Dear seqfans,

I am showing you a new sequence (new = not in OEIS) before
I submit it, in the hope of receiving some valuable input:

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).

Equivalently: values of n for which there exist two subsets
of the set of divisors of n, having the same sum.

Sequence contains, for example, all multiples of 6 (1+2=3),
all multiples of 20 (1+4=5), all multiples of 28 (1+2+4=7),
all multiples of 63 (1+9=3+7).

Sequence starts:

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,

Interestingly, the displayed terms agree with the displayed
terms of A051774 (shown below), except that the new
sequence does not contain the term 175. On second thought,
it is not that strange: A051774, according to its definition,
must also contain all multiples of 6, 20, 28, 63, etc.

The number of distinct sums of distinct divisors of n are
given in A119347 and the triangle of the actual sums are
given in A119348 (both already submitted).

Thanks for just reading this.
Emeric

---------------
A051774  Contracted numbers.
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, 175, 176, 180 (list)
OFFSET  1,1
COMMENT  n is said to be contracted if and only if there exist
distinct divisors d_1<d_2<...<d_k such that
d_1+d_2+...+d_(k-1) >= d_k.
CROSSREFS  Numbers not in A051772.
Sequence in context: A037363 A049094 A105289 this_sequence A097216 A023196 
A005835
Adjacent sequences: A051771 A051772 A051773 this_sequence A051775 A051776 
A051777
KEYWORD  nonn
AUTHOR  Alexander Benjamin Schwartz (QBOB(AT)aol.com), Dec 08 1999