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 A225154 #19 Aug 26 2025 18:28:03
%S A225154 1,2,4,7,11,14,18,23,27,32,38,43,49,55,62,68,75,82,90,97,105,113,121,
%T A225154 130,138,147,156,166,175,185,194,204,214,225,235,246,257,267,279,290,
%U A225154 301,313,325,336,349,361,373,385,398
%N A225154 Floor(Sum_{i=1..n} (Sum_{j=1..i} sqrt(1/j))).
%C A225154 The fact that a(n)/n diverges (it is greater than sqrt(n)) implies sum_{k>=1} 1/sqrt(k) is not Cesaro summable.
%H A225154 Balarka Sen, <a href="/A225154/b225154.txt">Table of n, a(n) for n = 1..500</a>
%F A225154 a(n) ~ 2*Sum_{k=1..n} sqrt(k) ~ (4/3) n^(3/2).
%o A225154 (PARI) for(n=1,100,print1(floor(sum(i=1,n,sum(j=1,i,1/sqrt(j))))","))
%o A225154 (PARI) a(n)=sum(j=1,n,(n+1-j)/sqrt(j))\1 \\ _Charles R Greathouse IV_, May 02 2013
%Y A225154 Cf. A022819, A025224.
%K A225154 nonn,easy,changed
%O A225154 1,2
%A A225154 _Balarka Sen_, Apr 30 2013