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
FORMULA
a(n) is the minimum k such that n^(1/2^k) is irrational.
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. A352780.
KEYWORD
nonn
AUTHOR
Ryan Jean, Mar 02 2022
STATUS
approved