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 A352080 a(n) is the number of times that the square root operation must be applied to n in order to reach an irrational number. 2
 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS a(1) is undefined because 1^(1/2^k) = 1 for all k. Column a(n)-1 has the first nonunit term in row n of A352780. - Peter Munn, Nov 15 2022 LINKS Table of n, a(n) for n=2..108. FORMULA a(n) is the minimum k such that n^(1/2^k) is irrational. a(n) = A007814(A052409(n)) + 1. - Amiram Eldar, Mar 03 2022 a(n) = A001511(A267116(n)). - Peter Munn, Nov 15 2022 EXAMPLE a(2) = 1 because sqrt(2) is irrational. a(16) = 3 because sqrt(16) = 16^(1/2) = 4, sqrt(sqrt(16)) = 16^(1/4) = 2, but sqrt(sqrt(sqrt(16))) = 16^(1/8) = sqrt(2), which is irrational. MATHEMATICA a[n_] := IntegerExponent[GCD @@ FactorInteger[n][[;; , 2]], 2] + 1; Array[a, 100, 2] (* Amiram Eldar, Mar 03 2022 *) PROG (PARI) a(n) = if (!issquare(n, &n), 1, a(n)+1); \\ Michel Marcus, Mar 03 2022 CROSSREFS Cf. A000290 (squares), A010052. See the formula section for the relationships with A001511, A007814, A052409, A267116. Cf. also A000037 (indices of 1's), A030140 (indices of 2's). Cf. A352780. Sequence in context: A074064 A275215 A304886 * A295632 A139549 A216915 Adjacent sequences: A352077 A352078 A352079 * A352081 A352082 A352083 KEYWORD nonn AUTHOR Ryan Jean, Mar 02 2022 STATUS approved

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Last modified May 27 20:22 EDT 2023. Contains 362986 sequences. (Running on oeis4.)