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A060665

Sigma(x) = n has exactly nine solutions.
(history; published version)

#9 by OEIS Server at Mon Sep 23 13:10:48 EDT 2019

LINKS

David A. Corneth, <a href="/A060665/b060665_1.txt">Table of n, a(n) for n = 1..10046</a> (first 8577 terms from Robert Israel, terms <= 7*10^6)

#8 by N. J. A. Sloane at Mon Sep 23 13:10:48 EDT 2019

STATUS

proposed

approved

Discussion

Mon Sep 23

13:10

OEIS Server: Installed new b-file as b060665.txt.  Old b-file is now b060665_1.txt.

#7 by David A. Corneth at Mon Sep 23 06:28:50 EDT 2019

STATUS

editing

proposed

Discussion

Mon Sep 23

06:45

David A. Corneth: a(n) doesn't quite tend to 700*n in the first 40000 terms. Can we approach a(n) a bit better?

#6 by David A. Corneth at Mon Sep 23 06:28:40 EDT 2019

COMMENTS

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

LINKS

Robert Israel, David A. Corneth, <a href="/A060665/b060665_1.txt">Table of n, a(n) for n = 1..10046</a> (first 8577 terms from Robert Israel, terms </a>= 7*10^6)

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

STATUS

approved

editing

#5 by N. J. A. Sloane at Mon Sep 23 01:58:52 EDT 2019

STATUS

proposed

approved

#4 by Robert Israel at Sun Sep 22 23:37:33 EDT 2019

STATUS

editing

proposed

#3 by Robert Israel at Sun Sep 22 23:37:28 EDT 2019

LINKS

Robert Israel, <a href="/A060665/b060665.txt">Table of n, a(n) for n = 1..8577</a>

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

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:30:31 EDT 2012

AUTHOR

_Robert G. Wilson v (rgwv(AT)rgwv.com), _, Apr 18 2001

Discussion

Fri Mar 30

17:30

OEIS Server: https://oeis.org/edit/global/156

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Sigma(x) = n has exactly nine solutions.

DATA

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

OFFSET

1,1

EXAMPLE

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

MATHEMATICA

a = Table[ 0, {20000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 20001, a[ [ s ] ]++ ], {n, 1, 20000} ]; Select[ Range[ 20000 ], a[ [ # ] ] == 9 & ]

CROSSREFS

Cf. A007370, A007371, A007372.

KEYWORD

nonn

AUTHOR

Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 18 2001

STATUS

approved