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%I #26 Feb 14 2015 21:04:28
%S 2,3,4,5,7,374,702,758,998,1542,1598,1778,1808,1830,1974,2378,2430,
%T 2910,3164,3182,3188,3216,3506,3540,3666,3698,3818,3846,3986,4196,
%U 4230,4574,4718,4782,5126,5324,5610,5738,5918,5952,6002,6174,6270,6404,6450,6510
%N Unitary untouchable numbers: us(x) = n has no solution where us(x) (A063919) is the sum of the proper unitary divisors of x.
%C Pomerance & Yang show that this sequence has positive lower density (in fact, greater than 10^-7) and upper density at most 0.40632. - _Charles R Greathouse IV_, Dec 28 2013
%H Donovan Johnson, <a href="/A063948/b063948.txt">Table of n, a(n) for n = 1..10000</a>
%H C. Pomerance and H.-S. Yang, <a href="http://www.math.dartmouth.edu/~carlp/uupaper3.pdf">On untouchable numbers and related problems</a>, 2012
%H C. Pomerance and H.-S. Yang, <a href="http://www.math.dartmouth.edu/~carlp/uupaper6.pdf">Variant of a theorem of Erdős on the sum-of-proper-divisors function</a>, Mathematics of Computation, to appear c. 2014
%F If us(x) = n > 1, then n^2 - 4x >= 0. - _Dean Hickerson_, Sep 04, 2001.
%t us[x_] := us[x] = Total[ Select[ Divisors[x], GCD[#, x/#] == 1 &]] - x; us[1] = 1; usQ[n_] := With[{xm = Ceiling[n^2/4]}, Catch[ Do[ If[us[x] == n, Throw[True]]; If[x == xm, Throw[False]], {x, 1, xm}]]]; A063948 = Reap[ Do[ If[ !usQ[n], Print[n]; Sow[n]], {n, 1, 6600}]][[2, 1]] (* _Jean-François Alcover_, Jun 22 2012 *)
%Y Cf. A034448, A063919, A064000.
%K nonn,nice
%O 1,1
%A _Felice Russo_, Sep 04 2001
%E More terms from _David W. Wilson_, Sep 05 2001
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