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A116959
a(n) is the smallest k>0 for which lcm(1,...,k) is greater than k^n.
1
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
OFFSET
1,1
COMMENTS
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.
a(n) must be prime. - Robert G. Wilson v, Aug 01 2010
EXAMPLE
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.
MAPLE
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;
MATHEMATICA
f[n_] := Block[{k = 1}, While[k^n >= LCM @@ Range@k, k++ ]; k]; Array[f, 57] (* Robert G. Wilson v, Aug 01 2010 *)
CROSSREFS
Complement is A179925. - Robert G. Wilson v, Aug 01 2010
Sequence in context: A245396 A144574 A082373 * A249505 A091305 A164319
KEYWORD
nonn
AUTHOR
Abraham Rashin, Mar 30 2006
STATUS
approved