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

1,1

Links

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

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 *)

Crossrefs

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

Sequence in context: A044907 A252079 A324276 * A261247 A153719 A024637

Adjacent sequences: A324274 A324275 A324276 * A324278 A324279 A324280

Keyword

nonn

Author

Amiram Eldar, Feb 20 2019

Status

approved