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Search: id:A116959
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| A116959 |
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a[n] is the smallest k>0 for which lcm(1,...,k) is greater than k^n. |
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1
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| 3, 5, 7, 11, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 125, 127, 131, 139, 149, 151, 163, 167, 169, 179, 181, 191, 193, 197, 211, 223, 229, 233, 239, 241, 251, 257, 263, 271, 277, 281, 283, 293, 307, 311, 313, 331, 337
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Useful in solution of the following problem (extended from a problem on the Rutgers Undergraduate Math Prize Exam 2006): Fix m, let S={n>0: q|n for all integer q between 1 and the m-th root of n inclusive}. Prove that S is bounded from above.
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EXAMPLE
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a(2)=5 because 60=lcm(1,2,3,4,5)>5^2=25 but lcm(1,...,k)<=k^2 for k=1,2,3,4.
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MAPLE
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L:=[1]: for i from 2 to 1000 do L:=[op(L), lcm(L[i-1], i)]: od: a:=[]: for j from 1 to 100 do for i from 1 while L[i]<=i^j do od: a:=[op(a), i]: od: a;
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CROSSREFS
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Adjacent sequences: A116956 A116957 A116958 this_sequence A116960 A116961 A116962
Sequence in context: A019449 A094615 A082373 this_sequence A091305 A085498 A128926
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KEYWORD
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nonn
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AUTHOR
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Abraham Rashin (avi.rashin(AT)gmail.com), Mar 30 2006
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