A056813 - OEIS

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A056813

Largest non-unitary prime factor of LCM[1,...,n]; i.e. the largest prime which occurs to power > 1 in prime factorization of LCM[1,..,n].

1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,4`
	COMMENTS	`For n>0, p(n) appears {(p(n+1))^2 - (p(n))^2} times [from n=(p(n))^2 to n=(p(n+1))^2 - 1], i.e., A000040(n) appears A069482(n) times[from n=A001248(n) to n=A084920(n+1)] - Lekraj Beedassy, Mar 31 2005` `a(n) is the largest prime factor of A045948(n). [From Matthew Vandermast, Oct 29 2008]`
	LINKS	`Table of n, a(n) for n=0..104.`
	FORMULA	`a(n)=p(w) if p(w)^2 <= n < p(w+1)^2.`
	EXAMPLE	`The j-th prime appears at the position of its square, at n=P(j)^2.`
	CROSSREFS	`Cf. A054041, A056170.` `Sequence in context: A137921 A064876 A105517 * A125269 A077430 A105513` `Adjacent sequences: A056810 A056811 A056812 * A056814 A056815 A056816`
	KEYWORD	`nonn`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu), Aug 28 2000`
	STATUS	`approved`

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Last modified May 20 23:29 EDT 2013. Contains 225465 sequences.