A109685 - OEIS

%I #6 Dec 15 2017 17:36:54

%S 16,25,64,243,120409,720801,5040025,4032064,362880940816,

%T 3628800213481,3991680051905536,47900160082546704,6227020800662405184,

%U 8717829120075164064361,1307674368000199069586496,2092278988800044062720986249,355687428096000138859491069121

%N Smallest nontrivial perfect power with same leading digits as n!.

%o (PARI) for(n=1,22,pp=0;lmin=n!;lmax=lmin;while(!pp,lexp=floor(log(lmax)/log(2));for(e=2,lexp,cmin=ceil((lmin)^(1/e));if(cmin<=floor((lmax)^(1/e)),if(pp,pp=min(cmin^e,pp),pp=cmin^e)));lmin*=10;lmax=lmax*10+9);print1(pp", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 22 2007

%K base,nonn

%O 1,1

%A _Jason Earls_, Aug 07 2005

%E More terms from _Ryan Propper_, Jun 13 2006

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 22 2007