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A253641
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Largest integer b such that n=a^b for some integer a; a(0)=a(1)=1 by convention.
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6
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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
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OFFSET
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0,5
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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