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%I #9 May 28 2020 05:26:49
%S 36,180,252,396,468,612,684,828,900,1044,1116,1260,1332,1476,1548,
%T 1692,1764,1800,1908,1980,2124,2196,2340,2412,2556,2628,2700,2772,
%U 2844,2988,3060,3204,3276,3420,3492,3600,3636,3708,3852,3924,4068,4140,4284,4356,4500,4572,4716,4788,4900
%N Exponential Zumkeller numbers: numbers whose exponential divisors can be partitioned into two disjoint subsets of equal sum.
%C First differs from A318100 at n = 49: 4900 is a term that is not an exponential pseudoperfect number.
%H Amiram Eldar, <a href="/A335218/b335218.txt">Table of n, a(n) for n = 1..10000</a>
%e 36 is a term since its exponential divisors, {6, 12, 18, 36}, can be partitioned into 2 disjoint sets whose sum is equal: 6 + 12 + 18 = 36.
%t dQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m]); expDivQ[n_, d_] := Module[{ft = FactorInteger[n]}, And @@ MapThread[dQ, {ft[[;; , 2]], IntegerExponent[d, ft[[;; , 1]]]}]]; eDivs[n_] := Module[{d = Rest[Divisors[n]]}, Select[d, expDivQ[n, #] &]]; ezQ[n_] := Module[{d = eDivs[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]]; Select[Range[10^4], ezQ]
%Y The exponential version of A083207.
%Y Subsequence of A129575.
%Y A054979 is a subsequence.
%Y Cf. A318100, A322791, A323343.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 27 2020
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