OFFSET
1,1
COMMENTS
From Amiram Eldar, Feb 13 2021: (Start)
Assuming that 5 is the only odd untouchable number, all the terms are of the form 2*p, where p is a prime.
Alanen (1972) calculated the first 70 terms of this sequence (terms below 5000). (End).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..9035 (terms below 10^6, calculated using data from Giovanni Resta; terms 1..1000 from Donovan Johnson)
Jack David Alanen, Empirical study of aliquot series, Ph.D Thesis, Yale University, 1972.
Giovanni Resta, Untouchable numbers (includes a list of the 150232 untouchable numbers below 10^6).
MATHEMATICA
seq[max_] := Module[{v = Table[0, {max}]}, Do[k = DivisorSigma[1, n] - n; If[2 <= k <= max, v[[k]]++], {n, 1, max^2}]; Select[Rest[Position[v, _?(# == 0 &)] // Flatten], PrimeOmega[#] == 2 &]]; seq[1000] (* Amiram Eldar, Feb 13 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Jul 24 2006
EXTENSIONS
More terms from Franklin T. Adams-Watters and Don Reble, Jul 28 2006
STATUS
approved