A324277 Infinitary untouchable numbers: numbers that are not the sum of aliquot infinitary divisors of any number.

2, 3, 4, 5, 38, 68, 80, 128, 158, 164, 188, 192, 206, 212, 224, 278, 290, 308, 326, 368, 380, 398, 416, 432, 458, 518, 530, 536, 542, 548, 578, 584, 600, 626, 632, 692, 702, 710, 752, 758, 770, 782, 788, 818, 822, 836, 852, 872, 896, 902, 926, 938, 968, 998

Offset: 1

Author

Amiram Eldar, Feb 20 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2256 (terms below 30000)

Crossrefs

Cf. A049417, A126168, A005114, A063948 (unitary), A324276 (bi-unitary), A324278 (exponential).

Programs

Mathematica

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_] := isigma[n] = Times @@ (fun @@@ FactorInteger[n]); untouchableQ[n_] := Catch[ Do[ If[n == isigma[k]-k, Throw[True]], {k, 0, (n-1)^2}]] === Null; Reap[ Table[ If[ untouchableQ[n], Sow[n]], {n, 2, 1000}]][[2, 1]] (* after Jean-François Alcover at A005114 *)