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a(n) is the smallest integer such that the geometric mean of the first n terms is >= n.
1

%I #2 Mar 30 2012 17:35:24

%S 1,4,7,10,12,14,18,20,23,26,29,31,34,36,40,42,45,47,50,53,56,59,61,64,

%T 66,69,72,75,78,80,83,85,89,91,93,97,99,102,105,107,110,113,115,119,

%U 121,123,127,129,132,134,137,140,143,145,149,150,154,156,159,162,165,167

%N a(n) is the smallest integer such that the geometric mean of the first n terms is >= n.

%C a(n) is approximately e * n, but the growth is a bit irregular.

%o (PARI) al(n)=local(r,t);vector(n,k,if(k==1,r=t=1,r*=(t=ceil(k^k/r));t))

%Y Cf. A178599.

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, May 30 2010