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A067085
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Floor[ sum 1..n {1/k^(1/2)}].
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2
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1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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A well known inequality is 2*n^1/2 - 2 < b(n) < 2*n^1/2 - 1
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EXAMPLE
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a(4) = floor [ 1+ 1/sqrt(2) + 1/ sqrt(3) + 1/ sqrt(4) ] = [2.78445705037617328890999314260681] = 2
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MATHEMATICA
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Table[ Floor[ Sum[1/k^(1/2), {k, 1, n} ]], {n, 1, 75} ]
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PROG
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(PARI) { s=0; for (n=1, 1000, s+=1/n^(1/2); write("b067085.txt", n, " ", floor(s)) ) } [From Harry J. Smith, May 10 2010]
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CROSSREFS
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Sequence in context: A048686 A090501 A126848 * A055086 A001462 A082462
Adjacent sequences: A067082 A067083 A067084 * A067086 A067087 A067088
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jan 07 2002
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EXTENSIONS
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More terms from Robert G. Wilson v, Jan 09 2002
Terms added by Harry J. Smith, May 10 2010
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STATUS
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approved
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