Lengths Of Runs In The #-Of-Divisors Sequence
Leroy Quet
qq-quet at mindspring.com
Wed Jul 18 23:44:20 CEST 2007
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Hello SeqFans,
could someone check and compute a hundred terms or so of the seq below?
=20
4,6,9,21,22,25,33,39,46,49,51,54,...
=20
Integers n whose "ordered concatenation" of all divisors (except 1 and n) i=
s a prime.
=20
n div. prime
4 -> 1,2,4 -> 2
6 -> 1,2,3,6 -> 23
9 -> 1,3,9 -> 3
21 -> 1,3,7,21 -> 37
22 -> 1,2,11,22 -> 211
25 -> 1,5,25 -> 5
33 -> 1,3,11,33 -> 311
39 -> 1,3,13,39 -> 313
...
26 is not a member :
=20
26 -> 1,2,13,26 -> 213 -> 1,3,71,213 -> 371 -> 1,7,53,371 -> 753 -> 1,3,251=
,753 -> 3251 is prime
=20
but 753 will be a member.
=20
=20
I like 54:
=20
54 -> 1,2,3,6,9,18,27,54 -> 23691827 prime
=20
Best,
=C9.
=20
-----
=20
(I've used Magma to compute the factorization, plus Edwin Clarkk's advice:
=20
> [Math-Fun]
>
> (...)
> Use for example the command Divisors(12345678); at this site
>
> http://magma.maths.usyd.edu.au/calc/
>
> and click on evaluate. You will get
>
> [ 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 14593, 29186, 43779,
> 87558, 131337, 262674, 685871, 1371742, 2057613, 4115226, 6172839,
> 12345678 ]
>
> Total time: 0.350 seconds, Total memory usage: 6.46MB
=20
=20
=20
Please do not send any message during this period as you will
not be able to check whether it has been received or not by
the mailing list robot. Anyway, they would be distributed
only after the servers are rebooted.
I will send a mail to the list so that everyone knows operations
are back to normal. Thanks in advance for your patience and
your discipline in that matter.
with my best regards,
Olivier GERARD
PS: As usual, any inquiries about this matter should be directed
to me (olivier.gerard at gmail.com or olivier.gerard at paris7.jussieu.fr)
and not to the list.
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D
Chers abonn=E9s de la liste seqfan
Arr=EAt temporaire du serveur h=E9bergeant la liste
JEUDI 12 Juillet 18h, heure de Paris, pour les fran=E7ais,
jusqu'au
VENDREDI 13 Juillet au matin (probablement 9h)
S'il vous plait, n'envoyez pas de message pendant cette p=E9riode,
vous ne pourriez pas savoir si il a =E9t=E9 bien re=E7u, et vous risqueriez
de provoquer une confusion ou des doublons.
J'enverrai un courier =E0 la liste quand la situation sera revenue
=E0 la normale.
Merci d'avance pour votre patience et votre discipline.
Cordialement,
Olivier GERARD
PS: Comme d'habitude, si vous avez des questions =E0 ce sujet, =E9crivez
moi directement (olivier.gerard at gmail.com ou
olivier.gerard at paris7.jussieu.fr ) et pas =E0 la liste.
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<DIV id=3DidOWAReplyText34525 dir=3Dltr>
<DIV dir=3Dltr><FONT face=3D"Courier New" color=3D#000000 size=3D2>Hello=20
SeqFans,</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>could someone check and =
compute a=20
hundred terms or so of the seq below?</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New"=20
size=3D2>4,6,9,21,22,25,33,39,46,49,51,54,...</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>Integers n whose "o=
rdered=20
concatenation" of all divisors (except 1 and n) is a prime.</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2> n  =
; =20
div. prime</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2> 4 ->=20
1,2,4 -> 2</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2> 6 -> 1,2,3,6&nb=
sp; =20
-> 23</FONT></DIV></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2> 9 -> 1,3,9 =
; =20
-> 3</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>21 -> 1,3,7,21 =
=20
-> 37</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>22 -> 1,2,11,22 ->=
=20
211</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>25 -> 1,5,25 &nb=
sp; =20
-> 5</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>33 -> 1,3,11,33 ->=
=20
311</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>39 -> 1,3,13,39 ->=
=20
313</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>...</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>26 is not a member :</FO=
NT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>26 -> 1,2,13,26 ->=
213 ->=20
1,3,71,213 -> 371 -> 1,7,53,371 -> 753 -> 1,3,251,753 -> 325=
1 is=20
prime</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>but 753 will be a=20
member.</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>I like 54:</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>54 -> 1,2,3,6,9,18,27=
,54 ->=20
23691827 prime</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>Best,</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>=C9.</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>-----</FONT></DIV>
<DIV dir=3Dltr> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>(I've used Magma to comp=
ute the=20
factorization, plus Edwin Clarkk's advice:</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>> [Math-Fun]</FONT></=
DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>></FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>> (...)</FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2>> Use for example the=
command=20
Divisors(12345678); at this site<BR>><BR>> <A=20
href=3D"/exchweb/bin/redir.asp?URL=3Dhttp://magma.maths.usyd.edu.au/calc/"=
=20
target=3D_blank>http://magma.maths.usyd.edu.au/calc/</A><BR>><BR>> an=
d click=20
on evaluate. You will get<BR>><BR>> [ 1, 2, 3, 6, 9, 18, 47, 94, 141,=
282,=20
423, 846, 14593, 29186, 43779,<BR>> 87558, 131337, 262674, 685871, 13717=
42,=20
2057613, 4115226, 6172839,<BR>> 12345678 ]<BR>><BR>> Total time: 0=
.350=20
seconds, Total memory usage: 6.46MB<BR><BR></FONT></DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT face=3D"Courier New" size=3D2></FONT> </DIV>
<DIV dir=3Dltr><FONT><FONT face=3D"Courier New" size=3D2>Please do not send=
any=20
message during this period as you will<BR>not be able to check whether it h=
as=20
been received or not by<BR>the mailing list robot. Anyway, they would=
be=20
distributed<BR>only after the servers are rebooted.<BR><BR>I will send a ma=
il to=20
the list so that everyone knows operations<BR>are back to normal. Tha=
nks=20
in advance for your patience and<BR>your discipline in that matter.<BR><BR>=
with=20
my best regards,<BR><BR>Olivier GERARD<BR><BR>PS: As usual, any inquiries a=
bout=20
this matter should be directed<BR>to me (olivier.gerard at gmail.com or=20
olivier.gerard at paris7.jussieu.fr)<BR>and not to the=20
list.<BR><BR>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR><BR>Chers=20
abonn=E9s de la liste seqfan<BR><BR>Arr=EAt temporaire du serveur h=E9berge=
ant la=20
liste<BR><BR>JEUDI 12 Juillet 18h, heure de Paris, pour les=20
fran=E7ais,<BR><BR>jusqu'au<BR><BR>VENDREDI 13 Juillet au matin (probableme=
nt=20
9h)<BR><BR><BR>S'il vous plait, n'envoyez pas de message pendant cette=20
p=E9riode,<BR>vous ne pourriez pas savoir si il a =E9t=E9 bien re=E7u, et v=
ous=20
risqueriez<BR>de provoquer une confusion ou des doublons.<BR>J'enverrai un=
=20
courier =E0 la liste quand la situation sera revenue<BR>=E0 la normale.<BR>=
<BR>Merci=20
d'avance pour votre patience et votre=20
discipline.<BR><BR><BR>Cordialement,<BR><BR>Olivier GERARD<BR><BR><BR>PS: C=
omme=20
d'habitude, si vous avez des questions =E0 ce sujet, =E9crivez<BR>moi direc=
tement=20
(olivier.gerard at gmail.com ou<BR>olivier.gerard at paris7.jussieu.fr ) et pas =
=E0 la=20
liste.<BR><BR><BR><BR></FONT></DIV></FONT>
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