A069584 - OEIS

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A069584

a(n) = n - largest perfect power <= n.

0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 0, 1, 2, 3, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`a(n) = 0 if n = m^p that is if n is a full power (square, cube etc.).` `As Catalan's conjecture is now proved, n=8=2^3, n+1=9=3^2 is the only solution for a(n+1) = a(n) = 0.`
	LINKS	`Eric Weisstein's World of Mathematics, Catalan's conjecture`
	CROSSREFS	`Cf. A001597, a(n)=n-A081676(n).` `Sequence in context: A128584 A080099 A127711 * A199238 A181347 A014587` `Adjacent sequences: A069581 A069582 A069583 * A069585 A069586 A069587`
	KEYWORD	`easy,nonn`
	AUTHOR	`Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 24 2002`
	EXTENSIONS	`Edited by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 26 2003`

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Last modified February 17 11:46 EST 2012. Contains 206011 sequences.