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Smallest n-th power > n!.
1

%I #8 Nov 25 2024 17:17:13

%S 2,4,8,81,243,729,16384,65536,1953125,9765625,48828125,2176782336,

%T 13060694016,678223072849,4747561509943,33232930569601,

%U 2251799813685248,18014398509481984,144115188075855872,12157665459056928801,109418989131512359209,10000000000000000000000,100000000000000000000000,1000000000000000000000000,108347059433883722041830251

%N Smallest n-th power > n!.

%H Robert Israel, <a href="/A087375/b087375.txt">Table of n, a(n) for n = 1..448</a>

%F a(n) = A214046(n)^n for n > 1. - _Robert Israel_, Nov 25 2024

%e a(5) = 243 as 243 = 3^5 > 5! > 2^5.

%p g:= proc(n) floor(1+(n!)^(1/n))^n end proc:

%p map(g, [$1..30]); # _Robert Israel_, Nov 25 2024

%Y Cf. A087374, A214046.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 09 2003

%E Corrected and extended by Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 25 2004