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%I A337740 #12 Sep 19 2020 14:14:16
%S A337740 73616,682592,2081824,3963968,4960448,5440192,6621632,8000704,8134208,
%T A337740 12979264,31297472,33736064,43955584,55691392,58433152,58904704,
%U A337740 160074368,254533504,263654656,266828032,267369728,272240768,352668416,353383168,357542656,431462656,530110208
%N A337740 Weird numbers (A006037) with an even sum of divisors that are not Zumkeller numbers (A083207).
%C A337740 Non-deficient numbers (A023196) with an even sum of divisors (A000203) that are neither pseudoperfect numbers (A005835) nor Zumkeller numbers (A083207).
%C A337740 Equivalently, numbers k such that sigma(k) >= 2*k and sigma(k) == 0 (mod 2), such that no subset of the aliquot divisors of k sums to k or to sigma(k)/2.
%H A337740 Amiram Eldar, <a href="/A337740/b337740.txt">Table of n, a(n) for n = 1..10000</a>
%e A337740 73616 is a term since sigma(73616) = 147312 is even and larger than 2 * 73616 = 147232. No subset of the aliquot divisors of 73616 sums to 73616 or to sigma(73616)/2 = 73656.
%t A337740 seqQ[n_] := Module[{d = Divisors[n], sum, c, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, c = CoefficientList[Product[1 + x^i, {i, d}], x]; c[[1 + 2*n]] == 0 && c[[1 + sum/2]] == 0]]; Select[Range[10^6], seqQ]
%Y A337740 Intersection of A006037 and A171641.
%Y A337740 Cf. A000203, A083207.
%K A337740 nonn
%O A337740 1,1
%A A337740 _Amiram Eldar_, Sep 17 2020

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