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

Author

Amarnath Murthy, Jan 07 2002

Keywords

• easy
• nonn

Examples

			a(4) = floor(1 + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4)) = floor(2.78445705037617328890999314260681) = 2.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Table[ Floor[ Sum[1/k^(1/2), {k, 1, n} ]], {n, 1, 75} ]

PARI

{ s=0; for (n=1, 1000, s+=1/n^(1/2); write("b067085.txt", n, " ", floor(s)) ) } \\ Harry J. Smith, May 10 2010

Formula

A well-known inequality is 2*n^1/2 - 2 < b(n) < 2*n^1/2 - 1.

Extensions

More terms from Robert G. Wilson v, Jan 09 2002

Terms added by Harry J. Smith, May 10 2010