A007372 - OEIS

%I M5142 #36 Nov 18 2024 04:35:43

%S 24,42,48,60,84,90,224,228,234,248,270,294,324,450,468,528,558,620,

%T 640,660,810,882,888,896,968,972,1020,1050,1104,1116,1140,1216,1232,

%U 1240,1274,1332,1392,1400,1452,1456,1464,1482,1524,1530,1600,1694,1716,1760

%N Numbers k such that sigma(x) = k has exactly 3 solutions.

%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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Amiram Eldar, <a href="/A007372/b007372.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Donovan Johnson)

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

%H Robert G. Wilson v, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>.

%t a = Table[ 0, {2500} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 2501, a[ [ s ] ]++ ], {n, 1, 2500} ]; Select[ Range[ 2500 ], a[ [ # ] ] == 3 & ]

%o (PARI) is(n)=sum(k=1,n,sigma(k)==n)==3 \\ _Charles R Greathouse IV_, Mar 09 2014

%o (PARI) is(k) = invsigmaNum(k) == 3 \\ _Amiram Eldar_, Nov 17 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A000203.

%Y Number of solutions: A007369 (0), A007370 (1), A007371 (2), this sequence (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

%K nonn

%O 1,1

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