A338277 - OEIS

%I #25 Aug 21 2021 19:56:53

%S 0,1,5,17,37,70,117,181,265,372,504,664,855,1079,1339,1637,1977,2361,

%T 2791,3271,3802,4388,5032,5735,6501,7333,8232,9202,10245,11364,12562,

%U 13841,15204,16654,18193,19824,21549,23372,25295,27321,29451,31690,34040,36502,39081,41778,44597,47539,50609,53807

%N Greatest integer whose square root is less than or equal to Sum_{j=0..n} sqrt(j).

%H Robert Israel, <a href="/A338277/b338277.txt">Table of n, a(n) for n = 0..2000</a>

%F a(n) ~ (4/9)*n^3 + (2/3)*n^2 + (4*zeta(-1/2)/3)*n^(3/2) + (11/36)*n + zeta(-1/2)*sqrt(n). - _Robert Israel_, Oct 28 2020

%p f:= n -> floor(add(sqrt(i),i=1..n)^2):

%p map(f, [$0..100]); # _Robert Israel_, Oct 28 2020

%t a[n_] := Floor[(Sum[ Sqrt[k], {k, 0, n}])^2]; Array[a, 50, 0]

%o (PARI) a(n) = floor(sum(j=0, n, sqrt(j))^2); \\ _Michel Marcus_, Oct 26 2020

%Y Cf. A025224.

%K nonn

%O 0,3

%A _Robert G. Wilson v_, Oct 21 2020