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. ------------------------------------------------------------------- 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