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%I #11 Jun 30 2020 05:33:22
%S 60,72,90,96,150,294,360,420,480,486,504,540,600,630,660,672,726,756,
%T 780,792,864,924,936,960,990,1014,1020,1050,1056,1092,1120,1140,1152,
%U 1170,1176,1188,1224,1248,1344,1350,1368,1380,1386,1400,1428,1440,1470,1500,1530
%N Infinitary Zumkeller numbers (A335197) whose number of divisors is not a power of 2.
%C Zumkeller numbers (A083207) whose number of divisors is a power of 2 (A036537) are also infinitary Zumkeller numbers (A335197), since all of their divisors are infinitary.
%H Amiram Eldar, <a href="/A335198/b335198.txt">Table of n, a(n) for n = 1..10000</a>
%e 72 is a term since its set of infinitary divisors, {1, 2, 4, 8, 9, 18, 36, 72}, can be partitioned into the two disjoint sets, {1, 2, 72} and {4, 8, 9, 18, 36}, whose sum is equal: 1 + 2 + 72 = 4 + 8 + 9 + 18 + 36 = 75.
%t infdivs[n_] := If[n == 1, {1}, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infZumQ[n_] := Module[{d = infdivs[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]]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; Select[Range[1500], ! pow2Q[DivisorSigma[0, #]] && infZumQ[#] &] (* after _Michael De Vlieger_ at A077609 *)
%Y Subsequence of A335197.
%Y Cf. A083207, A036537.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 26 2020
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