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A083210 Numbers with no subset of their divisors such that the complement has the same sum.

%I A083210 #29 Dec 02 2024 21:19:09
%S A083210 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 A083210 32,33,34,35,36,37,38,39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,
%U A083210 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 A083210 Numbers with no subset of their divisors such that the complement has the same sum.
%C A083210 A083206(a(n)) = 0; complement of A083207; deficient numbers (A005100) are a subset.
%C A083210 A179529(a(n)) = 0. [_Reinhard Zumkeller_, Jul 19 2010]
%H A083210 Antti Karttunen, <a href="/A083210/b083210.txt">Table of n, a(n) for n = 1..20000</a>
%H A083210 Reinhard Zumkeller, <a href="/A083206/a083206.txt">Illustration of initial terms</a>
%o A083210 (Python)
%o A083210 from itertools import count, islice
%o A083210 from sympy import divisors
%o A083210 def A083210_gen(startvalue=1): # generator of terms >= startvalue
%o A083210     for n in count(max(startvalue,1)):
%o A083210         d = divisors(n)
%o A083210         s = sum(d)
%o A083210         if s&1^1 and n<<1<=s:
%o A083210             d = d[:-1]
%o A083210             s2, ld = (s>>1)-n, len(d)
%o A083210             z = [[0 for _ in range(s2+1)] for _ in range(ld+1)]
%o A083210             for i in range(1, ld+1):
%o A083210                 y = min(d[i-1], s2+1)
%o A083210                 z[i][:y] = z[i-1][:y]
%o A083210                 for j in range(y,s2+1):
%o A083210                     z[i][j] = max(z[i-1][j],z[i-1][j-y]+y)
%o A083210                 if z[i][s2] == s2:
%o A083210                     break
%o A083210             else:
%o A083210                 yield n
%o A083210         else:
%o A083210             yield n
%o A083210 A083210_list = list(islice(A083210_gen(),30)) # _Chai Wah Wu_, Feb 13 2023
%o A083210 (PARI) is_A083210(n) = !A083206(n); \\ _Antti Karttunen_, Dec 02 2024
%Y A083210 Positions of 0's in A083206.
%Y A083210 Cf. A083207 (complement).
%Y A083210 Cf. A005100, A083211 (subsequences).
%K A083210 nonn
%O A083210 1,2
%A A083210 _Reinhard Zumkeller_, Apr 22 2003