gmf@uvacs.UUCP (07/22/84)
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.
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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