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A105209
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Nearest integer to the cube root of n.
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5
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1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
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OFFSET
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1,4
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REFERENCES
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Erwin Voellmy, Fünfstellige Logarithmen und Zahlentafeln, Orell Füssli Verlag, Zürich (1962).
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LINKS
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Seung-Jin Bang, Problem 10212, The American Mathematical Monthly, Vol. 99, No. 4 (1992), p. 361, Nearest Integer Zeta Functions, solution to Problem 10212, ibid., Vol. 101, No. 6 (1994), pp. 579-580.
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FORMULA
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Sum_{n>=1} 1/a(n)^s = 3*zeta(s-2) + zeta(s)/4^s, for s > 3 (Seung-Jin Bang, 1992). - Amiram Eldar, Oct 31 2020
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EXAMPLE
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a(16) = 3 because 16^(1/3) = 2.519842...
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MAPLE
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for n from 1 to 200 do printf(`%d, `, round(n^(1/3))) od: # James A. Sellers, Apr 21 2005
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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