A067085 a(n) = floor(Sum_{k=1..n} 1/k^(1/2)).

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

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