A060661 Numbers k such that sigma(x) = k has exactly 5 solutions.

72, 144, 192, 216, 588, 600, 648, 792, 936, 992, 1056, 1224, 1302, 1320, 1560, 1736, 1980, 2040, 2088, 2112, 2268, 2448, 2730, 2790, 2912, 3038, 3136, 3312, 3472, 3520, 3534, 3552, 3672, 3792, 3816, 3936, 4056, 4092, 4340, 4440, 4864, 4872, 4920, 4960

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			72 = sigma(30) = sigma(46) = sigma(51) = sigma(55) = sigma(71).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203.

Number of solutions: A007369 (0), A007370 (1), A007371 (2), A007372 (3), A060660 (4), this sequence (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

Programs

Mathematica

a = Table[ 0, {5000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 5001, a[ [ s ] ]++ ], {n, 1, 5000} ]; Select[ Range[ 5000 ], a[ [ # ] ] == 5 & ]
With[{upto=5000},Select[Union[Transpose[Select[Tally[DivisorSigma[ 1, Range[ upto]]],#[[2]]==5&]][[1]]],#<=upto&]] (* Harvey P. Dale, Jan 27 2015 *)

PARI

is(k) = invsigmaNum(k) == 5 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp