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 A063948 Unitary untouchable numbers: us(x) = n has no solution where us(x) (A063919) is the sum of the proper unitary divisors of x. 11
 2, 3, 4, 5, 7, 374, 702, 758, 998, 1542, 1598, 1778, 1808, 1830, 1974, 2378, 2430, 2910, 3164, 3182, 3188, 3216, 3506, 3540, 3666, 3698, 3818, 3846, 3986, 4196, 4230, 4574, 4718, 4782, 5126, 5324, 5610, 5738, 5918, 5952, 6002, 6174, 6270, 6404, 6450, 6510 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A034448, A063919, A064000. Sequence in context: A285888 A028986 A327324 * A113929 A220394 A082351 Adjacent sequences:  A063945 A063946 A063947 * A063949 A063950 A063951 KEYWORD nonn,nice AUTHOR Felice Russo, Sep 04 2001 EXTENSIONS More terms from David W. Wilson, Sep 05 2001 STATUS approved

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Last modified April 14 10:14 EDT 2021. Contains 342949 sequences. (Running on oeis4.)