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%I #14 Feb 18 2021 00:22:43
%S 2,3,4,5,38,68,80,96,98,128,138,146,158,164,180,188,192,206,208,210,
%T 212,222,224,248,264,278,290,300,304,308,324,326,328,338,360,374,380,
%U 390,398,416,418,420,430,432,458,476,480,488,498,516,518,530,536,542,548
%N Bi-unitary untouchable numbers: numbers that are not the sum of aliquot bi-unitary divisors of any number.
%H Amiram Eldar, <a href="/A324276/b324276.txt">Table of n, a(n) for n = 1..3591</a> (terms below 30000)
%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_] := bsigma[n] = Times @@ (fun @@@ FactorInteger[n]); untouchableQ[n_] := Catch[ Do[ If[n == bsigma[k]-k, Throw[True]], {k, 0, (n-1)^2}]] === Null; Reap[ Table[ If[ untouchableQ[n], Sow[n]], {n, 2, 550}]][[2, 1]] (* after Jean-François Alcover at A005114 *)
%Y Cf. A188999, A005114, A063948 (unitary), A324277 (infinitary), A324278 (exponential), A331970.
%K nonn
%O 1,1
%A _Amiram Eldar_, Feb 20 2019