[seqfan] Re: Unitary RMPN

[hv at crypt.org]

Hi, each prime factor of n must divide a(n), and each prime power dividing
a(n) must be >= n. That implies 72 divides a(6), and it is easy to show
72 and 144 do not satisfy the requirement but 216 does, so a(n)=216.

For n=10 we require 400 dividing a(10); working by hand, I found a better
solution a(10) ?= 2^5 . 3^3 . 5^3 . 7^2; I don't know if that's the first,
but it seems likely.

I don't know of an effective way to find these for the general case though,
or to verify a value is the first possible, other than by crude exhaustive
search.

Hugo

zbi74583.boat at orange.zero.jp wrote:
:    Hi,Seqfan
:
:    [ Unitary Rational Multiply Perfect Number ]
:
:    Definition of URMPN :
:    UnitarySigma(n)=k*n
:              Where k is rational number
:    Ex.
:    k=3/2
:    2,20,24,360,816,....
:    k=5/3
:    12,18,2^6*3*7*13,2^6*3^2*5*7*13,2^15*3^6*5*7*11*19*37*73*83*331
:
:    Definition of ((n+1)/n )URMPN :
:    UnitarySigma(m)=(n+1)/n*m
:             Wnere n is positive integer
:
:    Definition of Sequence a(n) :
:    The smallest number which is ((n+1)/n)URMPN
:    6,2,3,4,5,216,7,8,9,2^15*3^3*5^4*7^2*79*83*157*313*331,11,-,13,-,-,16,17,-,19,....
:             Where "-" means unknown
:
:    If n is prime power then a(n)=n
:
:    Could anuone confirm a(6) and a(10) and compute more terms which are not
:prime power?
:    I am sure that a(12) has many digit
:
:
:
:    Yasutoshi
:
:
:
:
:
:_______________________________________________
:
:Seqfan Mailing list - http://list.seqfan.eu/