%I #10 Mar 25 2023 05:30:26
%S 5390,7400,11830,17920,20230,25270,37030,43750,58870,67270,95830,
%T 117670,129430,154630,168070,196630,243670,260470,314230,352870,
%U 373030,436870,459270,482230,554470,658630,714070,742630,801430,831670,893830,1024870,1129030,1201270
%N Infinitary weird numbers (A306984) whose number of divisors is not a power of 2.
%C Weird numbers (A006037) whose number of divisors is a power of 2 (A036537) are also infinitary weird numbers (A306983), since all of their divisors are infinitary.
%H Amiram Eldar, <a href="/A335936/b335936.txt">Table of n, a(n) for n = 1..10000</a>
%t fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; infabQ[n_] := isigma[n] > 2*n; idivs[x_] := If[x == 1, 1, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infwQ[n_] := infabQ[n] && Module[{d = Most @ idivs[n]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; seq = {}; Do[If[!pow2Q[DivisorSigma[0, n]] && infwQ[n], AppendTo[sm n]], {n, 1, 10^5}]; s
%Y Intersection of A162643 and A306984.
%Y Cf. A006037, A036537, A077609, A335935.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jun 30 2020
%E More terms from _Amiram Eldar_, Mar 25 2023