A338277 Greatest integer whose square root is less than or equal to Sum_{j=0..n} sqrt(j).

0, 1, 5, 17, 37, 70, 117, 181, 265, 372, 504, 664, 855, 1079, 1339, 1637, 1977, 2361, 2791, 3271, 3802, 4388, 5032, 5735, 6501, 7333, 8232, 9202, 10245, 11364, 12562, 13841, 15204, 16654, 18193, 19824, 21549, 23372, 25295, 27321, 29451, 31690, 34040, 36502, 39081, 41778, 44597, 47539, 50609, 53807

Offset: 0

Author

Robert G. Wilson v, Oct 21 2020

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A025224.

Programs

Maple

f:= n -> floor(add(sqrt(i),i=1..n)^2):
map(f, [$0..100]); # Robert Israel, Oct 28 2020

Mathematica

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

PARI

a(n) = floor(sum(j=0, n, sqrt(j))^2); \\ Michel Marcus, Oct 26 2020

Formula

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