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%I #24 Feb 14 2023 08:55:22
%S 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,29,31,
%T 32,33,34,35,36,37,38,39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,
%U 61,62,63,64,65,67,68,69,71,72,73,74,75,76,77,79,81,82,83,85,86,87,89,91
%N Numbers with no subset of their divisors such that the complement has the same sum.
%C A083206(a(n)) = 0; complement of A083207; deficient numbers (A005100) are a subset.
%C A179529(a(n)) = 0. [_Reinhard Zumkeller_, Jul 19 2010]
%H Reinhard Zumkeller, <a href="/A083206/a083206.txt">Illustration of initial terms</a>
%o (Python)
%o from itertools import count, islice
%o from sympy import divisors
%o def A083210_gen(startvalue=1): # generator of terms >= startvalue
%o for n in count(max(startvalue,1)):
%o d = divisors(n)
%o s = sum(d)
%o if s&1^1 and n<<1<=s:
%o d = d[:-1]
%o s2, ld = (s>>1)-n, len(d)
%o z = [[0 for _ in range(s2+1)] for _ in range(ld+1)]
%o for i in range(1, ld+1):
%o y = min(d[i-1], s2+1)
%o z[i][:y] = z[i-1][:y]
%o for j in range(y,s2+1):
%o z[i][j] = max(z[i-1][j],z[i-1][j-y]+y)
%o if z[i][s2] == s2:
%o break
%o else:
%o yield n
%o else:
%o yield n
%o A083210_list = list(islice(A083210_gen(),30)) # _Chai Wah Wu_, Feb 13 2023
%Y Cf. A083211.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Apr 22 2003
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