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A335216 Bi-unitary Zumkeller numbers (A335215) that are not exponentially odd numbers (A268335).

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%I A335216 #7 May 27 2020 14:20:12
%S A335216 48,60,72,80,90,150,162,192,240,288,294,320,336,360,420,432,448,504,
%T A335216 528,540,560,576,600,624,630,648,660,720,726,756,768,780,792,800,810,
%U A335216 816,832,880,912,924,936,960,990,1008,1014,1020,1040,1050,1092,1104,1134,1140
%N A335216 Bi-unitary Zumkeller numbers (A335215) that are not exponentially odd numbers (A268335).
%C A335216 Zumkeller numbers (A083207) that are exponentially odd (A268335) are also bi-unitary Zumkeller numbers (A335215), since all of their divisors are bi-unitary.
%e A335216 48 is a term since it is not exponentially odd number (48 = 2^4 * 3 and 4 is even), and its set of bi-unitary divisors, {1, 2, 3, 6, 8, 16, 24, 48}, can be partitioned into 2 disjoint sets, whose sum is equal: 1 + 2 + 3 + 8 + 16 + 24 = 6 + 48.
%t A335216 uDivs[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; bDivs[n_] := Select[Divisors[n], Last @ Intersection[uDivs[#], uDivs[n/#]] == 1 &]; bzQ[n_] := Module[{d = bDivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bzQ[#] &]
%Y A335216 Subsequence of A335215.
%Y A335216 Cf. A083207, A268335, A290466.
%K A335216 nonn
%O A335216 1,1
%A A335216 _Amiram Eldar_, May 27 2020