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%I #14 Feb 18 2019 02:09:20
%S 18,162,450,882,1458,2178,2450,3042,4050,5202,6050,6498,7938,8450,
%T 9522,11250,13122,15138,17298,19602,22050,24642,27378,30258,33282,
%U 36450,39762,43218,46818,50562,54450,58482,61250,62658,66978,71442,76050,80802,85698
%N Non-deficient numbers with odd sigma such that the sum of the even divisors is twice the sum of the odd divisors.
%C Numbers which are non-deficient (2n <= sigma(n)) [A023196] such that sigma(n) [A000203] is odd and the sum of the even divisors [A074400] is twice the sum of the odd divisors [A000593].
%C The sequence of terms which are not of the form 72*k^2 + 72*k + 18 starts: 2450, 6050, 8450, 61250, 120050, 151250, 211250, 296450.
%H Donovan Johnson, <a href="/A171642/b171642.txt">Table of n, a(n) for n = 1..1000</a>
%H Peter Luschny, <a href="http://www.luschny.de/math/seq/ZumkellerNumbers.html"> Zumkeller Numbers</a>.
%e Example: divisors(18) = {1, 2, 3, 6, 9, 18}, sigma(18) = 39, and 2 + 6 + 18 = 2*(1 + 3 + 9).
%p with(numtheory): A171642 := proc(n) local k,s,a;
%p s := sigma(n); a := add(k,k=select(x->type(x,odd),divisors(n)));
%p if 3*a = s and 2*n <= s and type(s,odd) then n else NULL fi end:
%o (Python)
%o from sympy import divisors
%o A171642 = []
%o for n in range(1,10**5):
%o ....d = divisors(n)
%o ....s = sum(d)
%o ....if s % 2 and 2*n <= s and s == 3*sum([x for x in d if x % 2]):
%o ........A171642.append(n)
%o # _Chai Wah Wu_, Aug 20 2014
%Y Cf. A000203, A023196, A074400, A000593.
%Y Cf. A171641, A083207, A023196, A077591, A137933.
%K nonn
%O 1,1
%A _Peter Luschny_, Dec 14 2009
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