A060663 Numbers k such that sigma(x) = k has exactly 7 solutions.

240, 684, 744, 912, 1092, 1176, 1200, 1368, 1596, 2340, 2376, 2496, 2700, 3072, 3348, 4212, 5460, 5520, 5586, 5642, 5712, 6000, 6160, 6264, 6804, 6864, 7068, 7254, 7584, 7632, 7728, 8112, 8232, 8370, 8512, 8680, 8712, 8832, 8960, 9744, 9936

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			240 = sigma(114) = sigma(135) = sigma(158) = sigma(177) = sigma(203) = sigma(209) = sigma(239).
		

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), A060661 (5), A060662 (6), this sequence (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

Programs

Mathematica

a = Table[ 0, {10000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 10001, a[ [ s ] ]++ ], {n, 1, 10000} ]; Select[ Range[ 10000 ], a[ [ # ] ] == 7 & ]
With[{upto=10000},Select[Tally[DivisorSigma[1,Range[upto]]],#[[2]]==7 && #[[1]] <= upto&]][[All,1]]//Sort (* Harvey P. Dale, Jun 22 2019 *)

PARI

is(k) = invsigmaNum(k) == 7 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp