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