A060664 Numbers k such that sigma(x) = k has exactly 8 solutions.

336, 432, 672, 756, 840, 1536, 1620, 1764, 1848, 2280, 2394, 2604, 2808, 3264, 4080, 4480, 4860, 5328, 6528, 6624, 7128, 8316, 8568, 8880, 10608, 11040, 11448, 12288, 12420, 12636, 13176, 13200, 13248, 13536, 13860, 14196, 14208, 14448, 14700

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			336 = sigma(132) = sigma(140) = sigma(182) = sigma(188) = sigma(195) = sigma(249) = sigma(287) = sigma(299).
		

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), A060662 (6), A060663 (7), this sequence (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

Programs

Maple

N:= 30000: # to get terms <= N
V:= Vector(N):
for k from 1 to N-1 do
  t:= numtheory:-sigma(k);
  if t <= N then V[t]:= V[t]+1 fi
od:
select(t -> V[t]=8, [$1..N]); # Robert Israel, Sep 22 2019

Mathematica

a = Table[ 0, {20000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 20001, a[ [ s ] ]++ ], {n, 1, 20000} ]; Select[ Range[ 20000 ], a[ [ # ] ] == 8 & ]

PARI

is(k) = invsigmaNum(k) == 8 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp