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A067085 a(n) = floor(Sum_{k=1..n} 1/k^(1/2)). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
A well-known inequality is 2*n^1/2 - 2 < b(n) < 2*n^1/2 - 1.
EXAMPLE
a(4) = floor(1 + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4)) = floor(2.78445705037617328890999314260681) = 2.
MATHEMATICA
Table[ Floor[ Sum[1/k^(1/2), {k, 1, n} ]], {n, 1, 75} ]
PROG
(PARI) { s=0; for (n=1, 1000, s+=1/n^(1/2); write("b067085.txt", n, " ", floor(s)) ) } \\ Harry J. Smith, May 10 2010
CROSSREFS
Sequence in context: A361385 A126848 A232753 * A321578 A055086 A001462
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Jan 07 2002
EXTENSIONS
More terms from Robert G. Wilson v, Jan 09 2002
Terms added by Harry J. Smith, May 10 2010
STATUS
approved

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Last modified July 20 14:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)