%I #14 Feb 13 2021 06:28:17
%S 146,206,262,326,562,626,718,766,802,818,898,926,934,982,1046,1186,
%T 1318,1346,1418,1438,1522,1538,1642,1718,1766,1774,1822,1838,1894,
%U 2062,2078,2098,2174,2218,2258,2302,2306,2446,2498,2518,2602,2606,2614,2642,2762
%N Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number.
%C From _Amiram Eldar_, Feb 13 2021: (Start)
%C Assuming that 5 is the only odd untouchable number, all the terms are of the form 2*p, where p is a prime.
%C Alanen (1972) calculated the first 70 terms of this sequence (terms below 5000). (End).
%H Amiram Eldar, <a href="/A119379/b119379.txt">Table of n, a(n) for n = 1..9035</a> (terms below 10^6, calculated using data from Giovanni Resta; terms 1..1000 from Donovan Johnson)
%H Jack David Alanen, <a href="https://ir.cwi.nl/pub/9143">Empirical study of aliquot series</a>, Ph.D Thesis, Yale University, 1972.
%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/untouchable_number/">Untouchable numbers</a> (includes a list of the 150232 untouchable numbers below 10^6).
%t 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 *)
%Y Intersection of A001358 and A005114.
%K nonn
%O 1,1
%A _Tanya Khovanova_, Jul 24 2006
%E More terms from _Franklin T. Adams-Watters_ and _Don Reble_, Jul 28 2006