%I A125225
%S A125225 1,2,4,6,8,12,16,18,20,24,28,30,32,36,40,42,48,54,56,60,64,66,70,72,78,
%T A125225 80,84,88,90,96,100,104,108,112,120,126,128,132,140,144,150,156,160,162,
%U A125225 168,176,180,192,196,198,200,204,208,210,216,220,224,228,234,240,252
%N A125225 Numbers n such that n-1 can be represented as a sum of a subset of divisors 
               of n.
%C A125225 The definition is related to that for semiperfect numbers (A005835). 
               Every practical number (A005153) belongs to this sequence but not 
               necessarily vice versa; e.g., 70 is in this sequence but not practical. 
               Every number n in this sequence has sigma(n) >= 2n-1 (A103288) but, 
               despite being abundant, 102 is not in this sequence.
%D A125225 Such numbers can be used to construct inheritance puzzles of the type 
               described by Premchand Anne (1998). "Egyptian fractions and the inheritance 
               problem". The College Mathematics Journal 29 (4): 296-300.
%e A125225 70 is in this sequence because 70-1=69=35+14+10+7+2+1 and all numbers 
               in the sum are divisors of 70.
%Y A125225 Cf. A005835, A000225, A005153, A103288.
%Y A125225 Sequence in context: A058825 A087086 A103288 this_sequence A092903 A005153 
               A068563
%Y A125225 Adjacent sequences: A125222 A125223 A125224 this_sequence A125226 A125227 
               A125228
%K A125225 nonn
%O A125225 1,2
%A A125225 David Eppstein (eppstein(AT)ics.uci.edu), Jan 13 2007