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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 Harry J. Smith, Table of n, a(n) for n = 1..1000 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 Adjacent sequences: A067082 A067083 A067084 * A067086 A067087 A067088 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.)