A007370 - OEIS

%I M2319 #46 Nov 18 2024 03:44:46

%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 Wacław 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&amp;Stegun.pdf">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

%H Wacław Sierpiński, <a href="http://matwbn.icm.edu.pl/kstresc.php?tom=42&amp;wyd=10">Elementary Theory of Numbers</a>, Warszawa, 1964.

%H Robert 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

%o (PARI) is(k) = invsigmaNum(k) == 1 \\ _Amiram Eldar_, Nov 18 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A000203.

%Y Number of solutions: A007369 (0), this sequence (1), A007371 (2), A007372 (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_