[seqfan] Odd Amicable m-tuple
zbi74583.boat at orange.zero.jp
zbi74583.boat at orange.zero.jp
Mon Sep 26 08:12:11 CEST 2016
Hi,Seqfan
See Amicable Triple, Amicable Quadruple, Amicable 5-tuple.
A125490 A036471 A273928
They are all even.
I think that odd Amicable m-tuple must exist for any m.
I conjectured the size of them are the following.
"The size of odd Amicable m-tuple is almost the same as the size of 2*m
Multiple Perfect Number"
So,the smallest odd Amicable Triple has almost the same digit as the
smallest 6 MPN.
It may possible to compute the smallest odd Amicable Triple because 6 MPN is
not so large.
But to compute the smallest odd Amicable m-tuple for m=4 is impossible
because 8 MPN must have more digits.
The conjecture is the case of p=2 of the following.
"The size of Amicable m-tuple coprime to p is almost the same as the size of
m*p' MPN"
Where if p=Product p_i then p' =Product p_i/(p_i-1) p_i is Prime.
Ex. Size of Amicable Number coprime 2*3*5*7.
p'=2*2*3/2*5/4*7/6=35/4
So the smallest AN coprime 2*3*5*7 has the same digits as 9 MPN.
If someone compute the smallest odd Amicable Triple in this year then it
would be nice.
Because 2016 is one member of the smallest Amicable Triple.
Yasutoshi
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