cp's OEIS Frontend

A171642 Non-deficient numbers with odd sigma such that the sum of the even divisors is twice the sum of the odd divisors.

%I A171642 #21 Dec 21 2024 11:18:50
%S A171642 18,162,450,882,1458,2178,2450,3042,4050,5202,6050,6498,7938,8450,
%T A171642 9522,11250,13122,15138,17298,19602,22050,24642,27378,30258,33282,
%U A171642 36450,39762,43218,46818,50562,54450,58482,61250,62658,66978,71442,76050,80802,85698
%N A171642 Non-deficient numbers with odd sigma such that the sum of the even divisors is twice the sum of the odd divisors.
%C A171642 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 A171642 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 A171642 Donovan Johnson, <a href="/A171642/b171642.txt">Table of n, a(n) for n = 1..1000</a>
%H A171642 Peter Luschny, <a href="http://www.luschny.de/math/seq/ZumkellerNumbers.html">Zumkeller Numbers</a>.
%e A171642 Divisors(18) = {1, 2, 3, 6, 9, 18}, sigma(18) = 39, and 2 + 6 + 18 = 2*(1 + 3 + 9).
%p A171642 with(numtheory): A171642 := proc(n) local k,s,a;
%p A171642 s := sigma(n); a := add(k,k=select(x->type(x,odd),divisors(n)));
%p A171642 if 3*a = s and 2*n <= s and type(s,odd) then n else NULL fi end:
%o A171642 (Python)
%o A171642 from sympy import divisors
%o A171642 A171642 = []
%o A171642 for n in range(1, 10**5):
%o A171642     d = divisors(n)
%o A171642     s = sum(d)
%o A171642     if s % 2 and 2*n <= s and s == 3*sum([x for x in d if x % 2]):
%o A171642         A171642.append(n)
%o A171642 # _Chai Wah Wu_, Aug 20 2014
%Y A171642 Cf. A000203, A023196, A074400, A000593.
%Y A171642 Cf. A171641, A083207, A023196, A077591, A137933.
%K A171642 nonn
%O A171642 1,1
%A A171642 _Peter Luschny_, Dec 14 2009