A324276 Bi-unitary untouchable numbers: numbers that are not the sum of aliquot bi-unitary divisors of any number.

2, 3, 4, 5, 38, 68, 80, 96, 98, 128, 138, 146, 158, 164, 180, 188, 192, 206, 208, 210, 212, 222, 224, 248, 264, 278, 290, 300, 304, 308, 324, 326, 328, 338, 360, 374, 380, 390, 398, 416, 418, 420, 430, 432, 458, 476, 480, 488, 498, 516, 518, 530, 536, 542, 548

Offset: 1

Author

Amiram Eldar, Feb 20 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3591 (terms below 30000)

Crossrefs

Cf. A188999, A005114, A063948 (unitary), A324277 (infinitary), A324278 (exponential), A331970.

Programs

Mathematica

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 *)