id:A074198 - OEIS Search Results

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Largest k such that 1!*2!*3!*...*k! divides n!.

+0
2

1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14 (list; graph; listen)

	OFFSET	`1,2`
	FORMULA	`a(n) is asymptotic to sqrt(2n) and for n>300 a(n) = ceil(1/2+sqrt(1+8n)/2) (+0 or +1)`
	EXAMPLE	`18!/prod(i=1,7, i!) = 51051 but 18!/prod(i=1,8, i!) = 2431/1920 hence a(18)=7`
	PROGRAM	`(PARI) a(n)=if(n<0, 0, s=1; while(n!%prod(i=1, s, i!) == 0, s++); s-1)`
	CROSSREFS	`Cf. A088302, A074199.` `Sequence in context: A116458 A093875 A114214 this_sequence A048688 A092695 A033270` `Adjacent sequences: A074195 A074196 A074197 this_sequence A074199 A074200 A074201`
	KEYWORD	`easy,nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 17 2002`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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