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A335936 Infinitary weird numbers (A306984) whose number of divisors is not a power of 2. 1

%I

%S 5390,7400,11830,17920,20230,25270,37030,43750,58870,67270,95830,

%T 117670,129430,154630,168070,196630,243670,260470,314230

%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.

%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 Subsequence of A306984.

%Y Cf. A006037, A036537, A077609, A335935.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Jun 30 2020

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Last modified August 8 14:39 EDT 2022. Contains 356009 sequences. (Running on oeis4.)