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Let phi_m(x) denote the Euler totient function applied m times to x. Sequence gives the minimum number of iterations m such that phi_m(n) divides n.

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1, 1, 2, 1, 3, 1, 3, 1, 3, 2, 4, 1, 4, 2, 4, 1, 5, 1, 4, 2, 4, 3, 5, 1, 5, 3, 4, 2, 5, 3, 5, 1, 5, 4, 5, 1, 5, 3, 5, 2, 6, 3, 5, 3, 5, 4, 6, 1, 5, 4, 6, 3, 6, 1, 6, 2, 5, 4, 6, 3, 6, 4, 5, 1, 6, 4, 6, 4, 6, 4, 6, 1, 6, 4, 6, 3, 6, 4, 6, 2, 5, 5, 7, 3, 7, 4, 6, 3, 7, 4, 6, 4, 6, 5, 6, 1, 7, 4, 6, 4, 7, 5, 7, 3, 6 (list; graph; listen)

	OFFSET	`1,3`
	FORMULA	`It seems that sum(k=1, n, a(k)) is asymptotic to Cnlog(n) with C>1.`
	EXAMPLE	`phi(22) ->10 phi(10)->4 phi(4)->2 and 2 divides 22. Hence 3 iterations are needed and a(22) = 3`
	PROGRAM	`(PARI) a(n) = if(n<0, 0, c=1; s=n; while(n%eulerphi(s)>0, s=eulerphi(s); c++); c)`
	CROSSREFS	`Cf. A019294.` `Adjacent sequences: A073404 A073405 A073406 this_sequence A073408 A073409 A073410` `Sequence in context: A029236 A025820 A109704 this_sequence A049994 A135732 A084360`
	KEYWORD	`easy,nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 23 2002`

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Last modified October 7 08:31 EDT 2008. Contains 144667 sequences.

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