Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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