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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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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; listen)

	OFFSET	`1,4`
	COMMENT	`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]`
	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`
	EXAMPLE	`n=72=2.2.2.3.3: GCD[exponents]=GCD[3,2]=1. It deviates from Min of exponents(A051904).`
	MATHEMATICA	`Table[GCD @@ Last /@ FactorInteger[n], {n, 100}] (Chandler)`
	CROSSREFS	`Cf. A052410, A005361, A051903, A051904, A072411-A072414.` `Sequence in context: A145037 A158052 A158378 this_sequence A051904 A070012 A071178` `Adjacent sequences: A052406 A052407 A052408 this_sequence A052410 A052411 A052412`
	KEYWORD	`nonn`
	AUTHOR	`Eric Weisstein (eric(AT)weisstein.com)`
	EXTENSIONS	`More terms from Labos E. (labos(AT)ana.sote.hu), Jun 17 2002`

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Last modified December 2 11:54 EST 2009. Contains 167921 sequences.

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