A094227 - OEIS

%I #7 Aug 24 2022 14:33:04

%S 0,1,3,5,8,10,13,15,18,21,24,27,30,33,36,40,43,46,50,53,57,61,64,68,

%T 72,75,79,83,87,91,95,99,102,106,111,115,119,123,127,131,135,139,144,

%U 148,152,157,161,165,170,174,178,183,187,192,196,201,205,210,214,219,223

%N A prime-power sequence based on Gaussian asymptotic function.

%F a(n) = Floor[N[n*(n-1)^s(n)]] with s(n)=(Log[g[n]]-Log[n])/Log[n-1] and g[n]=(n*Pi*Log[n]-Sqrt[n^2*Pi+2*Pi^2*n])/Pi.

%F a(n) ~ n log n. - _Charles R Greathouse IV_, Aug 24 2022

%t g[n_]=(n*Pi*Log[n]-Sqrt[n^2*Pi+2*Pi^2*n])/Pi f[n_]=(Log[g[n]]-Log[n])/Log[n-1] a=Table[Floor[N[n*(n-1)^fa[n]]], {n, 3, 200}]

%o (PARI) s(n)=log(log(n) - sqrt(1/Pi+2/n))/log(n-1)

%o a(n)=n*(n-1)^s(n)\1 \\ _Charles R Greathouse IV_, Aug 24 2022

%K nonn,less

%O 3,3

%A _Roger L. Bagula_, May 28 2004