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A052409
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a(n) = largest integer power m for which a representation of the form n = k^m exists (for some k).
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21
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0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Greatest common divisor of all prime-exponents in canonical factorization of n for n>1: a(n)>1 iff n is a perfect power; a(A001597(k))=A025479(k). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 13 2002
a(1) set to 0 since there is no largest finite integer power m for which a representation of the form 1 = 1^m exists (infinite largest m). [From Daniel Forgues (squid(AT)zensearch.com), Mar 06 2009]
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..100000
Eric Weisstein's World of Mathematics, Power
Eric Weisstein's World of Mathematics, Perfect Power
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EXAMPLE
| n=72=2*2*2*3*3: GCD[exponents]=GCD[3,2]=1. It deviates from Min of exponents(A051904).
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MATHEMATICA
| Table[GCD @@ Last /@ FactorInteger[n], {n, 100}] (*Chandler*)
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CROSSREFS
| Cf. A052410, A005361, A051903, A051904, A072411-A072414.
Sequence in context: A145037 A158052 A158378 * A051904 A070012 A071178
Adjacent sequences: A052406 A052407 A052408 * A052410 A052411 A052412
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Labos E. (labos(AT)ana.sote.hu), Jun 17 2002
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