A361253 - OEIS

%I #24 Mar 17 2023 13:17:57

%S 0,1,2,3,2,5,6,7,8,3,10,11,12,13,14,15,2,17,18,19,20,21,22,23,24,5,26,

%T 27,28,29,30,31,32,33,34,35,6,37,38,39,40,41,42,43,44,45,46,47,48,7,

%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,8,65,66,67,68

%N If n = m^2 for some m > 1 then a(n) = a(m), otherwise a(n) = n.

%C All terms belong to A000037 U { 0, 1 }.

%C All terms of A000037 appear infinitely many times.

%C This sequence can be seen as the limit of the k-th iterate of A097448 as k tends to infinity.

%H Michael De Vlieger, <a href="/A361253/b361253.txt">Table of n, a(n) for n = 0..10000</a>

%F a(a(n)) = a(n).

%F a(n) <= A097448(n).

%F a(n) = 2 iff n belongs to A001146.

%F a(n) = 3 iff n belongs to A011764.

%F a(n) = 5 iff n belongs to A176594.

%e a(9) = a(3^2) = a(3) = 3 (as 3 is not a square).

%t nn = 120; Array[Set[a[#], #] &, 2, 0]; Do[If[IntegerQ[#], Set[k, a[#]], Set[k, n]] &[Sqrt[n]]; Set[a[n], k], {n, nn}]; Array[a, nn] (* _Michael De Vlieger_, Mar 06 2023 *)

%o (PARI) a(n) = my (m); { while (n > 1 && issquare(n, &m), n = m); return (n) }

%o (Python)

%o from sympy import integer_nthroot

%o def A361253(n):

%o     if n <= 1:

%o         return n

%o     a, b = integer_nthroot(c:=n,2)

%o     while b:

%o         a, b = integer_nthroot(c:=a,2)

%o     return c # _Chai Wah Wu_, Mar 17 2023

%Y Cf. A000037, A001146, A011764, A176594, A097448.

%K nonn,easy

%O 0,3

%A _Rémy Sigrist_, Mar 06 2023