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.
%I A352080 #32 Nov 16 2022 08:55:19 %S A352080 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, %T A352080 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, %U A352080 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 %N 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. %C A352080 a(1) is undefined because 1^(1/2^k) = 1 for all k. %C A352080 Column a(n)-1 has the first nonunit term in row n of A352780. - _Peter Munn_, Nov 15 2022 %F A352080 a(n) is the minimum k such that n^(1/2^k) is irrational. %F A352080 a(n) = A007814(A052409(n)) + 1. - _Amiram Eldar_, Mar 03 2022 %F A352080 a(n) = A001511(A267116(n)). - _Peter Munn_, Nov 15 2022 %e A352080 a(2) = 1 because sqrt(2) is irrational. %e A352080 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. %t A352080 a[n_] := IntegerExponent[GCD @@ FactorInteger[n][[;; , 2]], 2] + 1; Array[a, 100, 2] (* _Amiram Eldar_, Mar 03 2022 *) %o A352080 (PARI) a(n) = if (!issquare(n, &n), 1, a(n)+1); \\ _Michel Marcus_, Mar 03 2022 %Y A352080 Cf. A000290 (squares), A010052. %Y A352080 See the formula section for the relationships with A001511, A007814, A052409, A267116. %Y A352080 Cf. also A000037 (indices of 1's), A030140 (indices of 2's). %Y A352080 Cf. A352780. %K A352080 nonn %O A352080 2,3 %A A352080 _Ryan Jean_, Mar 02 2022