# [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

```