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%I #10 Jul 02 2020 03:51:52
%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 pseudoperfect numbers (A306983) whose number of divisors is not a power of 2.
%C Pseudoperfect numbers (A005835) whose number of divisors is a power of 2 (A036537) are also infinitary pseudoperfect numbers (A306983), since all of their divisors are infinitary.
%C First differs from A335198 at n = 77.
%H Amiram Eldar, <a href="/A335935/b335935.txt">Table of n, a(n) for n = 1..3000</a>
%e 60 is a term since its number of divisors is 12 which is not a power of 2, so not all of its divisors are infinitary, and it is the sum of its infinitary divisors: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
%t idivs[x_] := If[x == 1, 1, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infpspQ[n_] := Module[{d = Most @ idivs[n], x}, Plus @@ d >= n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] > 0]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; Select[Range[2, 500], !pow2Q[DivisorSigma[0,#]] && infpspQ[#] &]
%Y Subsequence of A005835 and A306983.
%Y Cf. A036537, A077609, A335198.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jun 30 2020
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