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A335939 Bi-unitary weird numbers (A292986) that are not exponentially odd numbers (A268335). 0

%I

%S 5390,7400,11830,20230,24010,25270,37030,58870,67270,95830,117670,

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

%N Bi-unitary weird numbers (A292986) that are not exponentially odd numbers (A268335).

%C Weird numbers (A006037) that are exponentially odd (A268335) are also bi-unitary weird numbers (A292986), since all of their divisors are bi-unitary.

%t fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); biuabQ[n_] := bsigma[n] > 2*n; f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; bweirdQ[n_] := biuabQ[n] && Module[{d = Most @ bdiv[n], x}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bweirdQ[#] &]

%Y Subsequence of A292986.

%Y Cf. A006037, A222266, A268335, A335936, A335938.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Jun 30 2020

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Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)