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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.

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

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OFFSET

1,1

COMMENTS

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.

No other terms below 2^30.

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

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

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.

CROSSREFS

The leftmost column in A328250.

Cf. A003415, A328248, A328320, A328321.

Sequence in context: A364109 A348180 A176080 * A346748 A348184 A065045

Adjacent sequences: A328299 A328300 A328301 * A328303 A328304 A328305

KEYWORD

nonn,more

AUTHOR

Antti Karttunen, Oct 12 2019

STATUS

approved