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A060665 Sigma(x) = n has exactly nine solutions. 1
360, 480, 1488, 1800, 1824, 2184, 2232, 2640, 3120, 3420, 3696, 3744, 3960, 4200, 5292, 5580, 5808, 6144, 7344, 7980, 8100, 8352, 8448, 8784, 9144, 10164, 10296, 11592, 11664, 11970, 12432, 13968, 14520, 14560, 15504, 15600, 15912, 16224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Do we have a(n) ~ c*n where c ~= 700? - David A. Corneth, Sep 23 2019

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10046 (first 8577 terms from Robert Israel, terms <= 7*10^6)

EXAMPLE

360 = sigma(120) = sigma(174) = sigma(184) = sigma(190) = sigma(267) = sigma(295) = sigma(319) = sigma(323) = sigma(359).

MAPLE

N:= 60000: # 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]=9, [$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[ [ # ] ] == 9 & ]

PROG

(PARI) upto(n) = {my(v = vecsort(vector(n, i, sigma(i))), res = List()); for(i = 2, #v - 9, if(v[i-1] <= n && v[i-1] != v[i] && v[i] == v[i + 8] && v[i] != v[i+9], listput(res, v[i]))); res} \\ David A. Corneth, Sep 23 2019

CROSSREFS

Cf. A007370, A007371, A007372.

Sequence in context: A031966 A137487 A069478 * A323024 A072414 A163569

Adjacent sequences:  A060662 A060663 A060664 * A060666 A060667 A060668

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Apr 18 2001

STATUS

approved

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Last modified October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)