

A324278


Exponential untouchable numbers: numbers that are not the sum of aliquot exponential divisors of any number.


2



1, 4, 8, 9, 16, 20, 25, 27, 28, 32, 40, 44, 45, 49, 52, 54, 63, 64, 68, 75, 76, 81, 88, 92, 96, 99, 104, 108, 116, 117, 121, 124, 125, 128, 136, 144, 147, 148, 152, 153, 160, 164, 169, 171, 172, 175, 176, 184, 188, 189, 192, 196, 200, 207, 208, 212, 216, 224
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OFFSET

1,2


COMMENTS

The terms are conjectural and based on a search for solutions to esigma(x)  x = k for k in the range of the data section and x < 10^12 (esigma(x)  x = A051377(x)  x = A126164(x) is the sum of aliquot exponential divisors of x).  Amiram Eldar, Jan 22 2020


LINKS

Table of n, a(n) for n=1..58.


MATHEMATICA

fun[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := esigma[n] = Times @@ fun @@@ FactorInteger[n]; untouchableQ[n_] := Catch[ Do[ If[n == esigma[k]k, Throw[True]], {k, 0, (n+1)^2}]] === Null; Reap[ Table[ If[ untouchableQ[n], Sow[n]], {n, 1, 130}]][[2, 1]] (* after JeanFrançois Alcover at A005114 *)


CROSSREFS

Cf. A051377, A126164, A005114, A063948 (unitary), A324276 (biunitary), A324277 (infinitary).
Sequence in context: A079432 A162215 A134344 * A119315 A010390 A003624
Adjacent sequences: A324275 A324276 A324277 * A324279 A324280 A324281


KEYWORD

nonn,changed


AUTHOR

Amiram Eldar, Feb 20 2019


EXTENSIONS

Data corrected by Amiram Eldar, Jan 22 2020


STATUS

approved



