A116959 - OEIS

%I #10 Jan 08 2021 10:42:03

%S 3,5,7,11,17,19,23,29,31,37,43,47,53,59,67,71,73,79,83,97,101,103,107,

%T 109,125,127,131,139,149,151,163,167,169,179,181,191,193,197,211,223,

%U 229,233,239,241,251,257,263,271,277,281,283,293,307,311,313,331,337

%N a(n) is the smallest k>0 for which lcm(1,...,k) is greater than k^n.

%C 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.

%C a(n) must be prime. - _Robert G. Wilson v_, Aug 01 2010

%e 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.

%p 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;

%t f[n_] := Block[{k = 1}, While[k^n >= LCM @@ Range@k, k++ ]; k]; Array[f, 57] (* _Robert G. Wilson v_, Aug 01 2010 *)

%Y Complement is A179925. - _Robert G. Wilson v_, Aug 01 2010

%K nonn

%O 1,1

%A Abraham Rashin, Mar 30 2006