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A338277
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Greatest integer whose square root is less than or equal to Sum_{j=0..n} sqrt(j).
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1
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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f:= n -> floor(add(sqrt(i), i=1..n)^2):
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MATHEMATICA
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a[n_] := Floor[(Sum[ Sqrt[k], {k, 0, n}])^2]; Array[a, 50, 0]
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PROG
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(PARI) a(n) = floor(sum(j=0, n, sqrt(j))^2); \\ Michel Marcus, Oct 26 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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