cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A328302 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 A328302 #14 Oct 14 2019 06:52:08
%S A328302 4,1,9,50,306,5831,20230,52283,286891,10820131,38452606
%N A328302 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 A328302 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 A328302 No other terms below 2^30.
%e A328302 a(2) = 1 is the least number that is squarefree already at the "zeroth derivative".
%e A328302 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 A328302 The leftmost column in A328250.
%Y A328302 Cf. A003415, A328248, A328320, A328321.
%K A328302 nonn,more
%O A328302 1,1
%A A328302 _Antti Karttunen_, Oct 12 2019