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For n > 1, a(n) is the least number > 0 for which it takes n-2 steps to reach a squarefree number by applying arithmetic derivative (A003415) zero or multiple times. a(1) = 4 is the least number for which no squarefree number is ever reached.
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%I #14 Oct 14 2019 06:52:08

%S 4,1,9,50,306,5831,20230,52283,286891,10820131,38452606

%N For n > 1, a(n) is the least number > 0 for which it takes n-2 steps to reach a squarefree number by applying arithmetic derivative (A003415) zero or multiple times. a(1) = 4 is the least number for which no squarefree number is ever reached.

%C The least number k such that A328248(k) = n. After the initial two terms, probably also the positions of records in A328248, that is, it is conjectured that the records in A328248 appear in order, with each new record one larger than previous.

%C No other terms below 2^30.

%e a(2) = 1 is the least number that is squarefree already at the "zeroth derivative".

%e 52283 = 7^2 * 11 * 97 is not squarefree, and applying A003415 successively 1-6 times yields numbers 20230, 19431, 14250, 21175, 15345, 15189. Only the last one of these 15189 = 3*61*83 is squarefree, and there are no numbers < 52283 that would produce as long (6) finite chain of nonsquarefree numbers, thus a(2+6) = 52283.

%Y The leftmost column in A328250.

%Y Cf. A003415, A328248, A328320, A328321.

%K nonn,more

%O 1,1

%A _Antti Karttunen_, Oct 12 2019