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From: gmf@uvacs.UUCP
Newsgroups: net.math
Subject: Divisor-Sum Problem
Message-ID: <1381@uvacs.UUCP>
Date: Sat, 21-Jul-84 17:06:26 EDT
Article-I.D.: uvacs.1381
Posted: Sat Jul 21 17:06:26 1984
Date-Received: Mon, 23-Jul-84 02:16:08 EDT
Lines: 35


This is a reposting.  I got no answers before, but I'm not sure if
this was because there weren't any, what with one thing and another.
-------------------------------------------------------------------


From: gmf Thu May 10 14:58:25 1984
(uvacs.1297) net.math : Iterated sums of digits of divisors

In the magazine * Abacus * for Winter, 1984 (v. 1, no. 2, Springer-Verlag)
there is the following problem on p. 73, attributed to Dr. Herta Freitag,
Hollins College, retired:

Let N(0) be an integer > 1.  Define N(K+1) as the sum of the  * digits *
of the divisors of N(K)  [not the sum of the divisors!!] .  Prove or
disprove that all such sequences end up with N(K+1) = 15, which then
repeats.  Example with N(0) = 12:

     K     N(K)     Divisors of N(K)
----------------------------------------
     0     12       1 2 3 4 6 12
     1     19       1 19
     2     11       1 11
     3      3       1 3
     4      4       1 2 4
     5      7       1 7
     6      8       1 2 4 8
     7     15       1 3 5 15
     8     15  which repeats forever

I ran a couple of hundred on a machine and it worked every time (didn't
always arrive at 15 in the same way, but arrived).  Does anyone know why
this is?

     Gordon Fisher