[seqfan] Re: Exactly two subsets of proper divisors of n sum to n.

[zak seidov]

By some mystery ;)
I've just submitted two related sequences,
so any comments may be refered to these A's.

Thanks,
Zak


%S A175015 12,18,42,56,66,100,176,196,208,348,372,444,460,
492,516,550,564,580,636, 708,732,736,738,774,804,812,820,846,852,868,876,928,948,954,968,992, 996,1036,1062,1068,1098,1148,1164,1204,1206,1212,1236,1278,1284,1308
%N A175015 Numbers n with property that exactly two subsets of proper divisors of n sum to n. 
%e A175015 n=12: proper divisors of 12 = {1,2,3,4,6} and 12=2+4+6=1+2+3+6. 
%Y A175015 Cf. A064771, A065205, A065235. 
%K A175015 nonn
%O A175015 1,1
%A A175015 Zak Seidov (zakseidov(AT)yahoo.com), Oct 29 2009

%S A175016 30,40,54,350,380,414,500,532,544,558,608,620,
644,666,726,740,1372,2002,
2190,2368,2370,2490,2624,2670,2910,3030,
3090,3162,3210,3250,3270,3390,3410,3430,3810,
3880,3930,4040,4110,4120,4170,4280,4360,4470,
4520,4530
%N A175016 Numbers n with property that exactly three subsets of proper divisors of n sum to n. 
%C A175016 Or numbers n such that A065205(n)=3. 
%e A175016 n=30: proper divisors of 30 = {1,2,3,5,6,10,15} and 
%e A175016 30=5+10+15=2+3+10+15=1+3+5+6+15. 
%Y A175016 Cf. A064771, A065205, A065235, A175015. 
%K A175016 nonn
%O A175016 1,1
%A A175016 Zak Seidov (zakseidov(AT)yahoo.com), Oct 29 2009
  

--- On Thu, 10/29/09, zak seidov <zakseidov at yahoo.com> wrote:

> From: zak seidov <zakseidov at yahoo.com>
> Subject: [seqfan]  Exactly two subsets of proper divisors of n sum to n.
> To: "seqfaneu" <seqfan at seqfan.eu>
> Date: Thursday, October 29, 2009, 8:07 AM
> Dear seqfans,
> 
> This is a draft of (possible) submission,
> pending your YEAS AND NAYS...
> 
> %N 
> Exactly two subsets of proper divisors of n sum to n.
> %C 
> Or numbers n such that A065205(n)=2.
> There are exactly 327 such numbers <10^4:
> 12,18,42,...,,9928,9948,9966, all even.
> %e 
> n=12: proper divisors of 12 =  {1,2,3,4,6} and
> 12=2+4+6=1+2+3+6\Q
> n=9966: proper divisors of 9966 = 
> {1,2,3,6,11,22,33,66,151,302,453,906,1661,3322,4983} and\Q
> 9966=1661+3322+4983=302+453+906+3322+4983.
> %C 
> Are there odd such numbers?
> Any theory behind this?
> 
> %Y
> Cf. A065205 Number of subsets of proper divisors of n that
> sum to n.\Q
> A064771 Let S(n)=set of divisors of n,excluding n;
> sequence gives n such that there is a unique subset of S(n)
> that sums to n.\Q
> A065235 Odd numbers in A064771.
> 
> %E
> Thanks ,
> Zak
> 
> 
> 
>       
> 
> 
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