The members of the sequence up to 10000 are
1, 13, 77, 489, 557, 1101, 1431, 2409, 8897.
It seems not to be in the OEIS.
Heuristically, the probability that sigma(x-1) + sigma(x+1) == 0 mod x
should be roughly 1/x, so we'd expect roughly log(n) members up to n.
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Good day,
In case you intend to publish it in the OEIS,
here is a mathematica formula to generate
the first terms of your sequence:
f[n_]:=Mod[Tr@Divisors[n-1]+Tr@Divisors[n+1],n]==0;
Select[Range[1000000], f]
{13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209}
--
Valeri
Two more :
{13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209, 2263024, 8910721}
V.
Up to 100,000,000 :
{13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209, 2263024, 8910721,
13685781, 17428321}
( none between 17,428,321 and 100,000,000 )
V.
Bonsoir,
The most difficult is not to get an OEIS sequence number,
it's to convince Mr Sloane that it's interesting
enough to be approved and published !
Just one more word before I leave this subject :
I dare disagree with Prof. Israel about 1 being the first
number of the sequence, because, 0 having no divisors
(or an infinity), its sum of divisors is undefined.
Ecrit à Paris le 10 février à 21h45.
Au revoir.
--
Valeri
>Up to 100,000,000 :
>
>{13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209, 2263024, 8910721,
>13685781, 17428321}
I confirm those and find no others below 500,000,000.
-- Richard
>>{13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209, 2263024, 8910721,
>>13685781, 17428321}
>I confirm those and find no others below 500,000,000.
The next is 962402769 and there are no others below 1,000,000,000.
-- Richard
>>>{13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209, 2263024, 8910721,
>>>13685781, 17428321}
>The next is 962402769 and there are no others below 1,000,000,000.
And I find none between 10^9 and 2x10^9, at which point I am giving up.
-- Richard