|
%I #19 Aug 10 2022 20:00:58
%S 1,2,9,64,125,1296,16807,262144,531441,10000000,214358881,5159780352,
%T 10604499373,289254654976,8649755859375,281474976710656,
%U 582622237229761,20822964865671168,799006685782884121
%N Smallest power of n >= n!.
%H Danny Rorabaugh, <a href="/A074181/b074181.txt">Table of n, a(n) for n = 1..447</a>
%F From _Danny Rorabaugh_, Apr 14 2015: (Start)
%F a(n) = n^A074184(n).
%F a(n) = n^ceiling(log_n(n!)) for n>1.
%F a(n) = n*A074182(n) = n^A060151(n) = n^(1 + A039960(n)) = n! + A111683(n) for n>2.
%F (End)
%t Join[{1},Table[n^Ceiling[Log[n,n!]],{n,2,20}]] (* _Harvey P. Dale_, Aug 10 2022 *)
%o (Sage) [1]+[n^ceil(log(factorial(n))/log(n)) for n in range(2,20)] # _Danny Rorabaugh_, Apr 14 2015
%o (PARI) a(n)=if(n>2,n^(logint(n!,n)+1),n) \\ _Charles R Greathouse IV_, Oct 11 2015
%Y Cf. A074182.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Aug 31 2002
%E More terms from _Jason Earls_, Sep 02 2002
|
