A361253 If n = m^2 for some m > 1 then a(n) = a(m), otherwise a(n) = n.

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, 27, 28, 29, 30, 31, 32, 33, 34, 35, 6, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 8, 65, 66, 67, 68

Offset: 0

Author

Rémy Sigrist, Mar 06 2023

Keywords

• nonn
• easy

Comments

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

All terms of A000037 appear infinitely many times.

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

Examples

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Python

from sympy import integer_nthroot
def A361253(n):
    if n <= 1:
        return n
    a, b = integer_nthroot(c:=n,2)
    while b:
        a, b = integer_nthroot(c:=a,2)
    return c # Chai Wah Wu, Mar 17 2023

Formula

a(a(n)) = a(n).

a(n) <= A097448(n).

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

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

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