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%I M2319 #38 Feb 25 2021 10:58:06
%S 1,3,4,6,7,8,13,14,15,20,28,30,36,38,39,40,44,57,62,63,68,74,78,91,93,
%T 102,110,112,121,127,133,138,150,158,160,162,164,171,174,176,183,194,
%U 195,198,200,204,212,217,222,230,242,255,256,258,260,266,278,282
%N Numbers k such that sigma(x) = k has a unique solution.
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%D W. Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964, p. 165.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Amiram Eldar, <a href="/A007370/b007370.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://plouffe.fr/simon/articles/Abramowitz&Stegun.pdf">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%H W. Sierpiński, <a href="http://matwbn.icm.edu.pl/kstresc.php?tom=42&wyd=10">Elementary Theory of Numbers</a>, Warszawa 1964.
%H R. G. Wilson, V, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>
%t a = Table[ 0, {250} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 251, a[ [ s ] ]++ ], {n, 1, 250} ]; Select[ Range[ 250 ], a[ [ # ] ] == 1 & ]
%o (PARI) list(lim)=my(v=vectorsmall(lim\1), u=List(), s); for(k=1,#v,s=sigma(k); if(s<=#v, v[s]++)); for(k=1,#v,if(v[k]==1, listput(u,k))); Vec(u) \\ _Charles R Greathouse IV_, Jun 15 2015
%Y Cf. A007369, A007371, A007372, etc.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_
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