A253641 Largest integer b such that n=a^b for some integer a; a(0)=a(1)=1 by convention.

1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 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, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,5

Comments

A000005(a(n))-1 yields the number of times n is listed in A072103, i.e., the number of ways it can be written differently as perfect power.

The same as A052409 if the convention is dropped. - R. J. Mathar, Jan 29 2015

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Example

a(4) = 2 since 4 = 2^2. a(64) = 6 since 64 = 2^6 (although also 64 = 4^3 = 8^2).
For any n, a(n) >= 1 since n = n^1.
Integers n = 0 and n = 1 can be written as n^b with arbitrarily large b; to remain consistent with the preceding formula and the comment, the conventional choice a(n) = 1 seemed the best one.

Prog

(PARI) A253641(n)=max(ispower(n), 1)
(Python)
from math import gcd
from sympy import factorint
def A253641(n): return gcd(*factorint(n).values()) if n>1 else 1 # Chai Wah Wu, Aug 13 2024

Crossrefs

Cf. A001597, A072103, A175064, A253642.

Sequence in context: A296134 A306694 A158052 * A158378 A052409 A327503

Adjacent sequences: A253638 A253639 A253640 * A253642 A253643 A253644

Keyword

nonn,easy

Author

M. F. Hasler, Jan 25 2015

Status

approved