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A074198
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Largest k such that 1!*2!*3!*...*k! divides n!.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) is asymptotic to sqrt(2*n) and for n>300 a(n) = ceil(1/2+sqrt(1+8*n)/2) (+0 or +1)
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EXAMPLE
| 18!/prod(i=1,7, i!) = 51051 but 18!/prod(i=1,8, i!) = 2431/1920 hence a(18)=7
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PROG
| (PARI) a(n)=if(n<0, 0, s=1; while(n!%prod(i=1, s, i!) == 0, s++); s-1)
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CROSSREFS
| Cf. A088302, A074199.
Sequence in context: A093875 A114214 A196383 * A196169 A048688 A092695
Adjacent sequences: A074195 A074196 A074197 * A074199 A074200 A074201
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 17 2002
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