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 A089363 #24 Jan 14 2025 03:15:55
%S A089363 3,16,50,145,407,1177,3508,10677,32967,102719,321798,1011538,3186390,
%T A089363 10050746,31730137,100228044,316713624,1001037551,3164497350,
%U A089363 10004755379,31632975601,100021893197,316274794667,1000101078155,3162495003354,10000467510250,31623782520067
%N A089363 Numbers of pairs (i, j), i, j > 1, such that i^j <= 10^n.
%C A089363 These numbers are related to the divergent series Sum_{k=2..r} n^(1/k) = n^(1/2) + n^(1/3) + ... + n^(1/r) for abs(n) > 0 and r=floor(log_2(n)).
%H A089363 Paolo Xausa, <a href="/A089363/b089363.txt">Table of n, a(n) for n = 1..1000</a>
%F A089363 a(n) = A089361(10^n) = Sum_{p >= 2} (floor(10^(n/p)) - 1). - _David Wasserman_, Sep 14 2005
%e A089363 There are 16 perfect powers <= 100: 2^2, 2^3, 3^2, 2^4, 4^2, 5^2, 3^3, 2^5, 6^2, 7^2, 2^6, 4^3, 8^2, 3^4, 9^2, 10^2. So a(2) = 16.
%t A089363 A089363[n_] := Sum[Floor[10^(n/j)] - 1, {j, 2, BitLength[10^n] - 1}];
%t A089363 Array[A089363, 30] (* _Paolo Xausa_, Jan 14 2025 *)
%o A089363 (PARI) plessn10(n,m=2) = { for(k=1,n, s=0; z = 10^k; r = sqrtint(z); for(x=m,r, for(y=2,r, p = floor(x^y); if(p<=z,s++) ) ); print1(s", ") ) }
%Y A089363 Cf. A089361.
%K A089363 nonn
%O A089363 1,1
%A A089363 _Cino Hilliard_, Dec 27 2003
%E A089363 More terms from _David Wasserman_, Sep 14 2005