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%I #52 Mar 12 2020 08:41:49
%S 1,2,6,11,34,48,112,139,274,794,860,2125,3259,3313,4842,9741,18637,
%T 17946,32306,41558,39471,66148,82046,131305,265464,313781,288660,
%U 339008,313761,366288,1287573,1451134,2014343,1824089,3743848,3371509,4510880,5976406
%N a(n) is the largest integer m such that m^n <= n^prime(n).
%C The sequence is not monotonic, for example a(18) < a(17).
%C Conjecture: there is no run of consecutive increasing terms with more than 17 terms.
%H Stefano Spezia, <a href="/A318199/b318199.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = floor(n^(prime(n)/n)).
%F a(n) = floor(A062481(n)^(1/n)).
%p Digits:= 2000:
%p a:= n-> floor(n^(ithprime(n)/n)):
%p seq(a(n),n=1..40); # _Muniru A Asiru_, Sep 17 2018
%t a[n_]:=Floor[n^(Prime[n]/n)]; Array[a,40]
%o (PARI) a(n) = sqrtnint(n^prime(n), n); \\ _Michel Marcus_, Mar 12 2020
%o vector(40, n, a(n))
%Y Cf. A000040, A062481, A333138.
%K nonn
%O 1,2
%A _Stefano Spezia_, Aug 21 2018