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%I #8 Mar 25 2023 05:28:13
%S 70,4030,5390,5830,7192,7400,7912,9272,10430,10570,10792,10990,11410,
%T 11690,11830,12110,12530,12670,13370,13510,13790,13930,14770,15610,
%U 15890,16030,16310,16730,16870,17272,17570,17920,17990,18410,18830,18970,19390,19670
%N Infinitary weird numbers: infinitary abundant numbers (A129656) that are not infinitary pseudoperfect numbers (A306983).
%C Differs from bi-unitary weird numbers from n >= 32 (a(32) = 17920 is not bi-unitary weird).
%H Amiram Eldar, <a href="/A306984/b306984.txt">Table of n, a(n) for n = 1..10000</a>
%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 &])]] ;s = {}; Do[d = Most[idivs[n]]; If[Total[d]<n,Continue[]]; c = SeriesCoefficient[ Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c < 1, AppendTo[s, n]], {n,2,10000}]; s
%Y Cf. A006037, A049417, A064114, A126168, A129656, A292986, A321146, A306983.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 18 2019