OFFSET
1,1
COMMENTS
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
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..10000
C. Pomerance and H.-S. Yang, On untouchable numbers and related problems, 2012
C. Pomerance and H.-S. Yang, Variant of a theorem of Erdős on the sum-of-proper-divisors function, Mathematics of Computation, to appear c. 2014
FORMULA
If us(x) = n > 1, then n^2 - 4x >= 0. - Dean Hickerson, Sep 04, 2001.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Felice Russo, Sep 04 2001
EXTENSIONS
More terms from David W. Wilson, Sep 05 2001
STATUS
approved