A060662 Numbers k such that sigma(x) = k has exactly 6 solutions.

168, 252, 288, 384, 768, 1248, 1584, 1860, 2052, 2480, 2904, 3906, 3968, 4116, 4176, 4224, 4256, 4284, 4392, 4416, 4620, 5824, 5850, 5856, 5928, 6084, 6192, 6216, 6600, 6636, 6660, 6888, 6944, 7104, 7182, 7308, 7840, 7992, 8184, 8976, 9114, 9480, 9856

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			168 = sigma(60) = sigma(78) = sigma(92) = sigma(123) = sigma(143) = sigma(167).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• 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), this sequence (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

Programs

Maple

N:= 10^4: # for terms <= N
V:= Vector(N):
for n from 1 to N-1 do
 s:= numtheory:-sigma(n);
 if s <= N then V[s]:= V[s]+1 fi
od:
select(t -> V[t]=6, [$1..N]); # Robert Israel, Nov 21 2019

Mathematica

a = Table[ 0, {10000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 10001, a[ [ s ] ]++ ], {n, 1, 10000} ]; Select[ Range[ 10000 ], a[ [ # ] ] == 6 & ]

PARI

is(k) = invsigmaNum(k) == 6 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp