A007372 Numbers k such that sigma(x) = k has exactly 3 solutions.

24, 42, 48, 60, 84, 90, 224, 228, 234, 248, 270, 294, 324, 450, 468, 528, 558, 620, 640, 660, 810, 882, 888, 896, 968, 972, 1020, 1050, 1104, 1116, 1140, 1216, 1232, 1240, 1274, 1332, 1392, 1400, 1452, 1456, 1464, 1482, 1524, 1530, 1600, 1694, 1716, 1760

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Keywords

• nonn

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
• Robert G. Wilson v, Letter to N. J. A. Sloane, Jul. 1992.

Crossrefs

Cf. A000203.

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).

Programs

Mathematica

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

PARI

is(n)=sum(k=1,n,sigma(k)==n)==3 \\ Charles R Greathouse IV, Mar 09 2014

PARI

is(k) = invsigmaNum(k) == 3 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp