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A338277 Greatest integer whose square root is less than or equal to Sum_{j=0..n} sqrt(j). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
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]
PROG
(PARI) a(n) = floor(sum(j=0, n, sqrt(j))^2); \\ Michel Marcus, Oct 26 2020
CROSSREFS
Cf. A025224.
Sequence in context: A053755 A162373 A146781 * A348228 A107199 A048209
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Oct 21 2020
STATUS
approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)