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A188666
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Largest m <= n such that lcm(m, m+1, ..., n) = lcm(1, 2, ..., n).
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6
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1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 7, 7, 8, 8, 9, 9, 11, 11, 11, 11, 13, 13, 13, 13, 16, 16, 16, 16, 16, 16, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 27, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 31, 32, 32, 37, 37, 37, 37, 37, 37
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OFFSET
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1,2
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COMMENTS
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By definition: A003418(n) = lcm(a(n), a(n)+1, ... n)
and lcm(m, m+1, ... n) < A003418(n) for m > a(n);
all terms are prime powers, cf. A000961: A010055(a(n)) = 1;
a(A110654(n)) = A000015(n);
floor(n/2)+1 <= a(n) < a(2*(a(n));
A000961(n+1) = a(2*A000961(n)) = a(A138929(n)), cf. formula.
A237709 gives number of occurrences of n-th prime power. - Reinhard Zumkeller, Feb 12 2014
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Least Common Multiple
Wikipedia, Least Common Multiple
Index entries for sequences related to lcm's
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FORMULA
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a(k) = A000961(k+1) for k: 2*A000961(k) <= k < 2*A000961(k+1), k > 0.
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PROG
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(Haskell)
import Data.List (elemIndices)
a188666 n = a188666_list !! (n-1)
a188666_list = g 1 a000961_list where
g n pps'@(pp:pp':pps) | n < 2*pp = pp : g (n+1) pps'
| otherwise = pp' : g (n+1) (pp':pps)
-- Alternative, rewriting the definition, but less efficient:
a188666' n = last $ elemIndices (f 1) $ map f [0..n] where
f from = foldl lcm 1 [from..n]
(PARI) A188666(n)=L=lcm(n=vector(n-1, k, k+1)); !for(m=1, #n, lcm(n[-m..-1])==L&&return(#n+2-m))\\ Rather illustrative than efficient. - M. F. Hasler, Jul 25 2015
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CROSSREFS
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Cf. A051173, A099996.
Sequence in context: A026802 A185329 A029031 * A328090 A029156 A241826
Adjacent sequences: A188663 A188664 A188665 * A188667 A188668 A188669
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Apr 25 2011
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STATUS
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approved
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