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Smallest number not yet used that is either a divisor or multiple of both n and a(n-1).
1

%I #5 Aug 12 2013 04:22:37

%S 1,2,6,12,60,3,21,168,504,2520,27720,4,52,364,5460,21840,371280,

%T 1113840,21162960,5,105,2310,53130,212520,1062600,13813800,124324200,

%U 7,203,6090,188790,3020640,33227040,564859680,35,1260,46620,885780,11515140,10,410

%N Smallest number not yet used that is either a divisor or multiple of both n and a(n-1).

%C This is apparently the smallest divisor of gcd(n,a(n-1)) not yet used if such exists, or lcm(n,a(n-1)) otherwise. This is a permutation of the positive integers. The required lemma is that there are arbitrarily long sequences where a(n) = lcm(n,a(n-1)).

%H Paul Tek, <a href="/A119862/b119862.txt">Table of n, a(n) for n = 1..10000</a>

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Jul 31 2006