[seqfan] Odd Amicable m-tuple

[zbi74583.boat at orange.zero.jp]

    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