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%I #11 Apr 10 2023 06:50:35
%S 704,1458,2394,7544,10184,46400,60416,106434,115182,118098,121014,
%T 125000,129762,141426,147258,150174,156006,158922,164754,176418,
%U 185166,190998,199746,202662,217242,220158,228906,237654,243486,246402,252234,260982,263898,278478
%N Numbers k whose bi-unitary divisors have an even sum which is larger than 2k, but they cannot be partitioned into two disjoint parts whose sums are equal.
%C The bi-unitary version of A171641.
%H Amiram Eldar, <a href="/A323342/b323342.txt">Table of n, a(n) for n = 1..10000</a>
%t f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[n_] := Select[Divisors[n], Last@Intersection[f@#, f[n/#]] == 1 &]; fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[n_] := If[n==1, 1, Times @@ (fun @@@ FactorInteger[n])]; seq={}; Do[s=bsigma[n]; If[OddQ[s] || s<=2n, Continue[]]; div = bdiv[n]; If[Coefficient[Times @@ (1 + x^div) // Expand, x, s/2] == 0, AppendTo[seq, n]], {n, 1, 10000}]; seq
%Y Cf. A171641, A188999, A292982, A323341, A323343, A323344.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jan 11 2019
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