[seqfan] Re: Who understands Granville numbers?
reinhard.zumkeller at gmail.com
Thu Oct 28 17:45:44 CEST 2010
with the following program I just calculated A118372(18) and A118372(19):
a118372_list = sPerfect 1 
sPerfect :: Int -> [Int] -> [Int]
sPerfect n ss =
case compare (sum $ filter ((== 0) . mod n) $ takeWhile (<
n) ss) n of
LT -> sPerfect (n+1) (n:ss)
EQ -> n:sPerfect (n+1) (n:ss)
GT -> sPerfect (n+1) ss
The list ss represents the set S, mentioned in the article of De Koninck
and Ivi´c, and in Walter Kehowski's contributions.
*S_perfect> take 19 a118372_list
A118372(18) = 393216 = 3 * 2^17
A118372(19) = 507904 = 31 * 2^14
The calculation for further terms would take more than 7 hours or so.
2010/10/28 Vladimir Shevelev <shevelev at bgu.ac.il>:
> About A118372. It seems very plausible that every term has the form a(n)=(2^k(n)-1)2^m(n) (maybe, this is known). If so, then there are at least 3 accompanying sequences which are not in OEIS:
> for 2^k(n)-1: 3 3 7 3 63 7 3 31 3 7 3 127...
> for k(n): 2 2 3 2 6 3 2 5 2 3 2 8...
> for m(n): 1 3 2 5 1 5 7 4 9 8 11 6...
> ----- Original Message -----
> From: Alonso Del Arte <alonso.delarte at gmail.com>
> Date: Thursday, October 28, 2010 1:10
> Subject: [seqfan] Who understands Granville numbers?
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> So I come across the concept of Granville numbers
>> in Jean-Marie de Koninck's book *Those Fascinating Numbers*. But
>> the concept
>> is giving me a headache. Is the definition of the set S
>> recursive (one
>> having to do a complete divisor tree to figure out membership)
>> or am I
>> completely misunderstanding it? I've had an easier time doing my
>> P.S. Daniel and I have signed up for a couple of slots for
>> Sequence of the
>> Day in November. Any SeqFan who hasn't yet chosen a Sequence of
>> the Day is
>> invited to sign up to choose it one day in November or December.
>> Seqfan Mailing list - http://list.seqfan.eu/
> Shevelev Vladimir
> Seqfan Mailing list - http://list.seqfan.eu/
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